A092277 - OEIS

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A092277

a(n) = 7*n^2 + n.

2

0, 8, 30, 66, 116, 180, 258, 350, 456, 576, 710, 858, 1020, 1196, 1386, 1590, 1808, 2040, 2286, 2546, 2820, 3108, 3410, 3726, 4056, 4400, 4758, 5130, 5516, 5916, 6330, 6758, 7200, 7656, 8126, 8610, 9108, 9620, 10146, 10686, 11240, 11808, 12390, 12986, 13596

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

First bisection of A219191. - Bruno Berselli, Nov 15 2012

LINKS

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 7*A000290(n) + n = A033582(n) + n. - Omar E. Pol, Dec 22 2008

a(n) = a(n-1) + 14*n - 6 with n > 0, a(0)=0. - Vincenzo Librandi, Nov 17 2010

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: 2*x*(4 + 3*x)/(1-x)^3.

E.g.f.: exp(x)*x*(8 + 7*x).

a(n) = 2*A022265(n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

EXAMPLE

From Bruno Berselli, Oct 27 2017: (Start)

After 0:

8 = -(1) + (2+3+4).

30 = -(1+2) + (3+4+5+6+7+8).

66 = -(1+2+3) + (4+5+6+7+8+9+10+11+12).

116 = -(1+2+3+4) + (5+6+7+8+9+10+11+12+13+14+15+16). (End)

PROG

(PARI) a(n)=7*n^2+n \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000290, A033582. - Omar E. Pol, Dec 22 2008

Cf. A022265, A219191.

Sequence in context: A071931 A333657 A074670 * A008469 A299279 A184323

Adjacent sequences: A092274 A092275 A092276 * A092278 A092279 A092280

KEYWORD

nonn,easy

AUTHOR

Evgeniy A. Chukhlomin (dkea(AT)yandex.ru), Feb 18 2004

STATUS

approved