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A015223
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Odd pentagonal pyramidal numbers.
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5
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1, 75, 405, 1183, 2601, 4851, 8125, 12615, 18513, 26011, 35301, 46575, 60025, 75843, 94221, 115351, 139425, 166635, 197173, 231231, 269001, 310675, 356445, 406503, 461041, 520251, 584325, 653455, 727833, 807651, 893101, 984375
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OFFSET
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0,2
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COMMENTS
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Also first bisection of A139757. - Bruno Berselli, Feb 13 2012
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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G.f.: (1 + 71*x + 111*x^2 + 9*x^3)/(1-x)^4. - Colin Barker, Feb 13 2012
a(n) = (2n+1)*(4n+1)^2 = A130656(4n+1). - Bruno Berselli, Feb 13 2012
From Ant King, Oct 23 2012: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 192.
Sum_{n>=0} 1/a(n) = (8*C - 2*Pi + Pi^2 - 4*log(2))/8, where C is Catalan's constant (A006752). (End)
E.g.f.: (1 + 74*x + 128*x^2 + 32*x^3)*exp(x). - G. C. Greubel, Nov 04 2017
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MATHEMATICA
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Table[((n+1)^3+(n+1)^2)/2, {n, 0, 200, 4}] (* Vladimir Joseph Stephan Orlovsky, May 21 2011 *)
CoefficientList[Series[(1 + 71 x + 111 x^2 + 9 x^3)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 15 2013 *)
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PROG
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(PARI) a(n)=(2*n+1)*(4*n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [(2n+1)*(4n+1)^2: n in [0..50]]; // G. C. Greubel, Nov 04 2017
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CROSSREFS
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Cf. A002411, A014799, A015224, A014800.
Sequence in context: A350245 A193252 A223452 * A129625 A133382 A199901
Adjacent sequences: A015220 A015221 A015222 * A015224 A015225 A015226
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian
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EXTENSIONS
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More terms from Erich Friedman
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STATUS
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approved
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