A029172 - OEIS

A029172

Expansion of 1/((1-x^2)*(1-x^4)*(1-x^5)*(1-x^7)).

1, 0, 1, 0, 2, 1, 2, 2, 3, 3, 4, 4, 6, 5, 8, 7, 10, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 31, 31, 36, 36, 42, 42, 48, 49, 55, 56, 62, 64, 71, 72, 80, 81, 90, 91, 100, 102, 111, 114, 123, 126, 136, 139, 150, 153, 165, 168, 180, 184, 197, 201, 214, 219, 233, 238, 252, 258

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OFFSET

0,5

COMMENTS

a(n) is the number of partitions of n into parts 2, 4, 5, and 7. - Hoang Xuan Thanh, Oct 08 2025

LINKS

Table of n, a(n) for n=0..67.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,1,-1,0,0,-2,0,0,-1,1,1,0,1,0,-1).

FORMULA

a(n) = floor((n^3+27*n^2+272*n+1344)/1680 - (n+6)*(n mod 2)/16 + ((4*n^3+3*n^2+3*n+1) mod 5)/5). - Hoang Xuan Thanh, Oct 08 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^5)(1-x^7)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 1, -1, 0, 0, -2, 0, 0, -1, 1, 1, 0, 1, 0, -1}, {1, 0, 1, 0, 2, 1, 2, 2, 3, 3, 4, 4, 6, 5, 8, 7, 10, 9}, 60] (* Harvey P. Dale, Jan 03 2015 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^5)*(1-x^7)) + O(x^68)) \\ Hoang Xuan Thanh, Oct 08 2025

CROSSREFS

Sequence in context: A035454 A161228 A214130 * A384178 A240864 A241322

Adjacent sequences: A029169 A029170 A029171 * A029173 A029174 A029175

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Hoang Xuan Thanh, Oct 08 2025

STATUS

approved