A014773 Squares of odd heptagonal numbers.

1, 49, 3025, 6561, 35721, 55225, 162409, 219961, 485809, 613089, 1147041, 1385329, 2325625, 2725801, 4239481, 4862025, 7144929, 8059921, 11336689, 12623809, 17147881, 18896409, 24950025, 27258841, 35153041, 38130625, 48205249, 51969681, 64593369, 69272329

Offset: 1

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A000566, A014637, A014640, A014792.

Programs

Mathematica

Table[SeriesCoefficient[x (1 + 48 x + 2972 x^2 + 3344 x^3 + 17262 x^4 + 5648 x^5 + 8396 x^6 + 560 x^7 + 169 x^8)/((1 - x)^5 (1 + x)^4), {x, 0, n}], {n, 30}] (* Michael De Vlieger, Dec 17 2015 *)

PARI

Vec(x*(1+48*x+2972*x^2+3344*x^3+17262*x^4+5648*x^5+8396*x^6+560*x^7+169*x^8) / ((1-x)^5*(1+x)^4) + O(x^40)) \\ Colin Barker, Dec 17 2015

Formula

From Colin Barker, Dec 17 2015: (Start)

a(n) = 1/2*(200*n^4-920*n^3+1578*n^2-1196*n+338) for n even.

a(n) = 1/2*(200*n^4-520*n^3+498*n^2-208*n+32) for n odd.

G.f.: x*(1+48*x+2972*x^2+3344*x^3+17262*x^4+5648*x^5+8396*x^6+560*x^7+169*x^8) / ((1-x)^5*(1+x)^4).

(End)

Extensions

More terms from Erich Friedman.