A029144 - OEIS

A029144

Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)).

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 7, 7, 9, 10, 11, 13, 14, 16, 18, 20, 22, 24, 27, 29, 32, 35, 38, 41, 45, 48, 52, 56, 60, 65, 69, 74, 79, 84, 90, 95, 102, 107, 114, 121, 127, 135, 142, 150, 158, 166, 175, 183, 193, 202, 212, 222, 232, 243, 254, 265, 277

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OFFSET

0,6

COMMENTS

a(n) is the number of partitions of n into parts 2, 3, 5, and 7. - Joerg Arndt, Oct 01 2025

LINKS

Table of n, a(n) for n=0..62.

Milan Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,0,-1,-1,0,0,0,0,1,1,0,-1).

FORMULA

a(n) = floor((2*n^3+51*n^2+390*n+1960)/2520 - (n mod 2)/8 + ((n+2) mod 3)/9). - Hoang Xuan Thanh, Sep 30 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^7)), {x, 0, 60}], x] (* Harvey P. Dale, Oct 28 2011 *)

PROG

(Maxima) a(n):=floor((2*n^3+51*n^2+390*n+2020)/2520+((-1)^mod(n, 5)-floor(mod(n, 5)/4))/5); /* Tani Akinari, Nov 13 2012 */

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)) + O(x^90)) \\ Jinyuan Wang, Mar 18 2020

(PARI) a(n) = (2*n^3+51*n^2+390*n+1960 - 315*(n%2) + 280*((n+2)%3))\2520 \\ Hoang Xuan Thanh, Sep 30 2025

CROSSREFS

Sequence in context: A264396 A007360 A359320 * A173244 A304114 A390512

Adjacent sequences: A029141 A029142 A029143 * A029145 A029146 A029147

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved