

A123596


Squares alternating with triangular numbers.


4



0, 0, 1, 1, 4, 3, 9, 6, 16, 10, 25, 15, 36, 21, 49, 28, 64, 36, 81, 45, 100, 55, 121, 66, 144, 78, 169, 91, 196, 105, 225, 120, 256, 136, 289, 153, 324, 171, 361, 190, 400, 210, 441, 231, 484, 253, 529, 276, 576, 300, 625, 325, 676, 351, 729, 378, 784, 406, 841, 435
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OFFSET

0,5


COMMENTS

Rearrangement of A054686.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, 3, 0, 1).


FORMULA

a(2*n) = n^2, a(2*n+1) = (n^2+n)/2.
From R. J. Mathar, Feb 12 2010: (Start)
a(n) = 3*a(n2)  3*a(n4) + a(n6).
G.f.: x^2*(1+x+x^2)/((1x)^3*(1+x)^3). (End)
a(n) = (3*n^21+(n^2+1)*(1)^n)/16.  Luce ETIENNE, May 30 2015


MATHEMATICA

CoefficientList[Series[x^2*(1+x+x^2)/((1x)^3*(1+x)^3)], {x, 0, 50}], x] (* or *) Table[(3*n^21+(n^2+1)*(1)^n)/16, {n, 0, 50}] (* G. C. Greubel, Oct 26 2017 *)


PROG

(PARI) {a(n) = if(n%2, (n^21)/8, n^2/4)} \\ Michael Somos, Nov 18 2006
(MAGMA) [(3*n^21+(n^2+1)*(1)^n)/16: n in [0..10]]; // G. C. Greubel, Oct 26 2017


CROSSREFS

Cf. A002620, A124093.
Sequence in context: A103825 A073238 A010655 * A309460 A200361 A222471
Adjacent sequences: A123593 A123594 A123595 * A123597 A123598 A123599


KEYWORD

nonn


AUTHOR

Peter Hansen (babyskbaby(AT)web.de), Nov 14 2006


EXTENSIONS

Edited by Michael Somos, and several other correspondents, Nov 14 2005


STATUS

approved



