

A260810


a(n) = n^2*(3*n^2  1)/2.


6



0, 1, 22, 117, 376, 925, 1926, 3577, 6112, 9801, 14950, 21901, 31032, 42757, 57526, 75825, 98176, 125137, 157302, 195301, 239800, 291501, 351142, 419497, 497376, 585625, 685126, 796797, 921592, 1060501, 1214550, 1384801, 1572352, 1778337, 2003926, 2250325, 2518776
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OFFSET

0,3


COMMENTS

Pentagonal numbers with square indices.
After 0, a(k) is a square if k is in A072256.


LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

G.f.: x*(1 + x)*(1 + 16*x + x^2)/(1  x)^5.
a(n) = a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5).
a(n) = A245288(2*n^2).
a(n) = A001318(2*n^21) with A001318(1)=0.


MAPLE

A260810:=n>n^2*(3*n^2  1)/2: seq(A260810(n), n=0..50); # Wesley Ivan Hurt, Apr 25 2017


MATHEMATICA

Table[n^2 (3 n^2  1)/2, {n, 0, 40}]
LinearRecurrence[{5, 10, 10, 5, 1}, {0, 1, 22, 117, 376}, 40] (* Vincenzo Librandi, Aug 23 2015 *)


PROG

(PARI) vector(40, n, n; n^2*(3*n^21)/2)
(Sage) [n^2*(3*n^21)/2 for n in (0..40)]
(MAGMA) [n^2*(3*n^21)/2: n in [0..40]];
(MAGMA) I:=[0, 1, 22, 117, 376]; [n le 5 select I[n] else 5*Self(n1)10*Self(n2)+10*Self(n3)5*Self(n4)+Self(n5): n in [1..40]]; // Vincenzo Librandi, Aug 23 2015


CROSSREFS

Subsequence of A001318 and A245288 (see Formula field).
Cf. A000326, A193218 (first differences).
Cf. A000583 (squares with square indices), A002593 (hexagonal numbers with square indices).
Cf. A232713 (pentagonal numbers with pentagonal indices), A236770 (pentagonal numbers with triangular indices).
Sequence in context: A299580 A289350 A100930 * A274610 A290800 A251930
Adjacent sequences: A260807 A260808 A260809 * A260811 A260812 A260813


KEYWORD

nonn,easy


AUTHOR

Bruno Berselli, Jul 31 2015


STATUS

approved



