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A060544
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Centered 9-gonal (or nonagonal) numbers. Every third triangular number, starting with a(1)=1.
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25
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1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, 1711, 1891, 2080, 2278, 2485, 2701, 2926, 3160, 3403, 3655, 3916, 4186, 4465, 4753, 5050, 5356, 5671, 5995, 6328, 6670, 7021, 7381, 7750, 8128, 8515, 8911, 9316
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Triangular numbers not == 0 (mod 3). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 13 2005
Shallow diagonal of triangular spiral in A051682. - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
Equals the triangular numbers convolved with [1, 7, 1, 0, 0, 0,...]. [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), May 29 2009]
Centered enneagonal numbers. - Omar E. Pol, Oct 03 2011
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for two-way infinite sequences
Index entries for sequences related to centered polygonal numbers
Eric Weisstein's World of Mathematics, Marion's Theorem
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1)
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FORMULA
| a(n) = C(n, 0)+9C(n, 1)+9C(n, 2); binomial transform of (1, 9, 9, 0, 0, 0, .....). a(n)=(9n^2+9n+2)/2. G.f. x*(1+7*x+x^2)/(1-x)^3. - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
a(n) = C(3n, 3)/n = (3n-1)*(3n-2)/2 = a(n-1)+9(n-1) = A060543(n, 3) = A006566(n)/n = A025035(n)/A025035(n-1) = A027468(n-1)+1 = A000217(3n-2).
a(1-n)=a(n).
Narayana transform (A001263) of [1, 9, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
a(n-1) = Pochhammer(4,3*n)/(Pochhammer(2,n)*Pochhammer(n+1,2*n)).
a(n-1) = 1/Hypergeometric([-3*n,3*n+3,1],[3/2,2],3/4). -- Peter Luschny, Jan 09 2012
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MAPLE
| H := n -> simplify(1/hypergeom([-3*n, 3*n+3, 1], [3/2, 2], 3/4)); A060544 := n -> H(n-1); seq(A060544(i), i=1..19); -- Peter Luschny, Jan 09 2012
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MATHEMATICA
| Transpose[Partition[Accumulate[Range[150]], 3]][[1]] [From Harvey P. Dale (hpd1(AT)nyu.edu), Nov 01 2009]
FoldList[#1 + #2 &, 1, 9 Range@ 50] (* Robert G. Wilson v, Feb 02 2011 *)
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PROG
| (PARI) a(n)=(3*n-1)*(3*n-2)/2
(PARI) { for (n=1, 1000, write("b060544.txt", n, " ", (3*n - 1)*(3*n - 2)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]
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CROSSREFS
| Cf. A001263, A027468, A081266, A190152.
Sequence in context: A177720 A117464 A081273 * A088406 A169879 A054112
Adjacent sequences: A060541 A060542 A060543 * A060545 A060546 A060547
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001
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EXTENSIONS
| Additional description from Terry Trotter, Apr 06 2002
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