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 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 (list; graph; refs; listen; history; text; internal format)
 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(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). a(n) = A245288(2*n^2). a(n) = A001318(2*n^2-1) 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^2-1)/2) (Sage) [n^2*(3*n^2-1)/2 for n in (0..40)] (MAGMA) [n^2*(3*n^2-1)/2: n in [0..40]]; (MAGMA) I:=[0, 1, 22, 117, 376]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): 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

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Last modified October 27 01:02 EDT 2020. Contains 338035 sequences. (Running on oeis4.)