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A258582 a(n) = n*(2*n + 1)*(4*n + 1)/3. 3
0, 5, 30, 91, 204, 385, 650, 1015, 1496, 2109, 2870, 3795, 4900, 6201, 7714, 9455, 11440, 13685, 16206, 19019, 22140, 25585, 29370, 33511, 38024, 42925, 48230, 53955, 60116, 66729, 73810, 81375, 89440, 98021, 107134, 116795, 127020, 137825, 149226, 161239, 173880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First bisection of the square pyramidal numbers (A000330).

LINKS

Table of n, a(n) for n=0..40.

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: x*(5 + 10*x + x^2)/(1 - x)^4.

a(n) = A000330(2*n).

Sum_{n>0} 1/a(n) = 3*(6 - Pi - 4*log(2)) = 0.25745587...

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Nov 18 2015

a(n) = A006918(4*n-1) = A053307(4*n-1) = A228706(4*n-1) for n>0. [Bruno Berselli, Nov 18 2015]

a(n) = Sum_{k=1..2*n} k^2 (see the first comment).  E.g.f. exp(x)*(5*x+ 20*x^2/2+16*x^3/3!). - Wolfdieter Lang, Mar 13 2017

MAPLE

A258582:=n->n*(2*n + 1)*(4*n + 1)/3: seq(A258582(n), n=0..50); # Wesley Ivan Hurt, Nov 17 2015

MATHEMATICA

Table[(1/3) n (2 n + 1) (4 n + 1), {n, 0, 45}]

PROG

(PARI) vector(100, n, n--; n*(2*n+1)*(4*n+1)/3) \\ Altug Alkan, Nov 06 2015

(PARI) concat(0, Vec((5*x + 10*x^2 + x^3)/(1 - x)^4 + O(x^50))) \\ Altug Alkan, Nov 06 2015

(MAGMA) [n*(2*n+1)*(4*n+1)/3: n in [0..50]]; // Wesley Ivan Hurt, Nov 17 2015

CROSSREFS

Cf. A000330, A001477, A005408, A016813, A053126 (partial sums), A100157.

Sequence in context: A273480 A164015 A128302 * A288679 A071252 A174002

Adjacent sequences:  A258579 A258580 A258581 * A258583 A258584 A258585

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 06 2015

STATUS

approved

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Last modified January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)