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A261191
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40-gonal numbers: a(n) = 38*n*(n-1)/2 + n.
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5
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0, 1, 40, 117, 232, 385, 576, 805, 1072, 1377, 1720, 2101, 2520, 2977, 3472, 4005, 4576, 5185, 5832, 6517, 7240, 8001, 8800, 9637, 10512, 11425, 12376, 13365, 14392, 15457, 16560, 17701, 18880, 20097, 21352, 22645, 23976, 25345, 26752, 28197, 29680, 31201
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OFFSET
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0,3
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COMMENTS
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According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 40).
The 4th number of the sequence, 117, is also the 10th pentagonal number (see A000326). The next number of the series, 232, is also the 9th decagonal number (see A001107), while 576 is the 25th square number (see A000290). The 12th number of the sequence, 2101, is the 23rd 11-gonal number (see A051682).
From Bruno Berselli, Aug 21 2015: (Start)
a(n) and a(n) - 2*n + 1 provide the numbers m such that 19*m + 81 is a square.
Partial sums of the numbers of the type 38*h + 1 (quadrisections of A113541 and A151979). (End)
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = n*(19*n - 18).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n > 2. - Colin Barker, Aug 11 2015
G.f.: -x*(37*x+1) / (x-1)^3. - Colin Barker, Aug 11 2015
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MAPLE
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A261191:=n->38*n*(n-1)/2+n: seq(A261191(n), n=0..50); # Wesley Ivan Hurt, Aug 15 2015
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MATHEMATICA
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Table[n (19 n - 18), {n, 0, 45}] (* Bruno Berselli, Aug 21 2015 *)
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PROG
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(JavaScript) function a(n){return 38*n*(n-1)/2+n}
(PARI) concat(0, Vec(-x*(37*x+1)/(x-1)^3 + O(x^100))) \\ Colin Barker, Aug 11 2015
(PARI) first(m)=my(v=vector(m, i, i--; 38*i*(i-1)/2+i)); v; \\ Anders Hellström, Aug 13 2015
(MAGMA) [n*(19*n-18): n in [0..45]]; // Vincenzo Librandi, Aug 12 2015
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CROSSREFS
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Sequence in context: A235893 A192791 A235886 * A260601 A234921 A199807
Adjacent sequences: A261188 A261189 A261190 * A261192 A261193 A261194
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KEYWORD
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nonn,easy
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AUTHOR
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Sergey Pavlov, Aug 11 2015
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STATUS
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approved
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