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A152767
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3 times 10-gonal (or decagonal) numbers: 3n(4n-3).
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10
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0, 3, 30, 81, 156, 255, 378, 525, 696, 891, 1110, 1353, 1620, 1911, 2226, 2565, 2928, 3315, 3726, 4161, 4620, 5103, 5610, 6141, 6696, 7275, 7878, 8505, 9156, 9831, 10530, 11253, 12000, 12771, 13566, 14385, 15228, 16095, 16986
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Jan. 1910 p. 47 (Problem 1052).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 12*n^2 - 9*n = 3*A001107(n).
a(n)=a(n-1)+24*n-21, n>0. [From Vincenzo Librandi, Nov 26 2010]
3*A172078(n) = n*a(n)-sum_{k=0..n-1} a(k). - Bruno Berselli, Dec 12 2010
a(n) = sum[A001539(k), k=0..n-1]-sum[4*A002939(k), k=0..n-1] if n>0 (see References, Problem 1052). - Bruno Berselli, Dec 08 2010 - Jan 21 2011
G.f.: -3*x*(1+7*x)/(x-1)^3.
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EXAMPLE
| For n=8, a(8)=(1*3+5*7+9*11+..+29*31)-(2*4+6*8+10*12+..+26*28) = 696 (see Problem 1052 in References). - Bruno Berselli, Dec 12 2010
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MATHEMATICA
| s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 24}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 02 2009]
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CROSSREFS
| Cf. A001107, A139271.
3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A153783, A153448, A153875.
Sequence in context: A132084 A012009 A001800 * A195029 A180816 A035328
Adjacent sequences: A152764 A152765 A152766 * A152768 A152769 A152770
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 15 2008
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