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A051624
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12-gonal (or dodecagonal) numbers: n(5n-4).
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41
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0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Zero followed by partial sums of A017281. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
L. Hogben, Choice and Chance by Cardpack and Chessboard. Vol. 1, Chanticleer Press, NY, 1950, p. 36.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=n*(5*n-4).
G.f.: x*(1+9*x)/(1-x)^3.
a(n) = Sum_{k=0..n-1} 10*k+1. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]
a(n)=10*n+a(n-1)-9 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+10 od: seq(a[n], n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 10}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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PROG
| (MAGMA) [ n eq 1 select 0 else Self(n-1)+10*(n-2)+1: n in [1..43] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]
(PARI) a(n)=(5*n-4)*n \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
| First differences of A007587.
Cf. A093645 ((10, 1) Pascal, column m=2). Partial sums of A017281.
Cf. n-gonal numbers: A000217, A000290, A000326, A000566, A000567, A001106, A001107, A051682, A051865-A051876.
Sequence in context: A079561 A131543 A063296 * A039338 A118337 A032604
Adjacent sequences: A051621 A051622 A051623 * A051625 A051626 A051627
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 09 1999
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