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A015222 Even square pyramidal numbers. 1
14, 30, 140, 204, 506, 650, 1240, 1496, 2470, 2870, 4324, 4900, 6930, 7714, 10416, 11440, 14910, 16206, 20540, 22140, 27434, 29370, 35720, 38024, 45526, 48230, 56980, 60116, 70210, 73810, 85344, 89440, 102510, 107134, 121836, 127020 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Square pyramidal numbers k*(k + 1)*(2*k + 1)/6 are even if and only when k is congruent to 0 or 3 mod 4. [From Artur Jasinski, Oct 22 2008]

LINKS

Table of n, a(n) for n=1..36.

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

FORMULA

Even entries in A000330.

Contribution from Artur Jasinski, Oct 22 2008: (Start)

(2*k + 1)/(k + 2)*Binomial(k + 2, 5) if k congruent to 0 or 3 mod 4

k*(k + 1)*(2*k + 1)/6 if k congruent to 0 or 3 mod 4

(End)

G.f. 2*x*(7+x*(8+x*(34+x*(8+7*x)))))/ ((-1+x)^4*(1+x)^3) [From Harvey P. Dale, May 05 2011]

Contribution from Ant King, Oct 17 2012: (Start)

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

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6)+128.

(End)

6*a(n) = (1+2*n)*(8*n^2+8*n-6*(-1)^n*n+3-3*(-1)^n). - R. J. Mathar, Oct 17 2012

MATHEMATICA

Select[ Table[ n(n+1)(2n+1)/6, {n, 100} ], EvenQ ]

Select[Rest[CoefficientList[Series[(x(x+1))/(x-1)^4, {x, 0, 80}], x]], EvenQ]  (* Harvey P. Dale, May 05 2011 *)

CROSSREFS

Cf. A000330.

Sequence in context: A075208 A228124 A293391 * A054103 A161454 A156203

Adjacent sequences:  A015219 A015220 A015221 * A015223 A015224 A015225

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Erich Friedman.

G.f. adapted to the offset by Bruno Berselli, May 16 2011

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)