A015225 Odd hexagonal pyramidal numbers.

1, 7, 95, 161, 525, 715, 1547, 1925, 3417, 4047, 6391, 7337, 10725, 12051, 16675, 18445, 24497, 26775, 34447, 37297, 46781, 50267, 61755, 65941, 79625, 84575, 100647, 106425, 125077, 131747, 153171, 160797, 185185, 193831, 221375, 231105

Offset: 1

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Crossrefs

Intersection of A002412 (hexagonal pyramidal) and A005408 (odd numbers).

Programs

Mathematica

LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,7,95,161,525,715,1547},36] (* Ant King, Oct 25 2012 *)

PARI

a(n)=(8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24 \\ Charles R Greathouse IV, Jul 30 2016

Formula

Odd numbers of the form n*(n+1)*(4n-1)/6.

From Ant King, Oct 25 2012: (Start)

a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).

a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.

a(n) = (8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24.

G.f.: x*(1+6*x+85*x^2+48*x^3+103*x^4+10*x^5+3*x^6) / ((1-x)^4*(1+x)^3). (End)

E.g.f.: (1/6)*(-9 - 6*x - 24*x^2 + 18*exp(x) + ( - 9 + 12*x + 36*x^2 + 32*x^3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 30 2016

Extensions

More terms from Erich Friedman.