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A015225 Odd hexagonal pyramidal numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

FORMULA

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

Contribution 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

MATHEMATICA

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

PROG

(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

CROSSREFS

Sequence in context: A221384 A243679 A327843 * A183521 A036337 A186378

Adjacent sequences:  A015222 A015223 A015224 * A015226 A015227 A015228

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Erich Friedman.

STATUS

approved

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Last modified October 18 15:41 EDT 2019. Contains 328162 sequences. (Running on oeis4.)