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A062786
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Centered 10-gonal numbers.
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14
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1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Deleting the least significant digit yields the (n-1)-st triangular number: a(n) = 5n(n-1)+1 = 10{n(n-1)/2} +1 = 10*T(n-1) +1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 11 2003
All divisors of a(n) are congruent to 1 or -1, modulo 10; that is, they end in the decimal digit 1 or 9. Proof: If p is an odd prime different from 5 then 5n^2 - 5n + 1 = 0 (mod p) implies 25(2n - 1)^2 = 5 (mod p), whence p = 1 or -1 (mod 10). - Nick Hobson Nov 13 2006
Centered decagonal 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 sequences related to centered polygonal numbers
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1)
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FORMULA
| 5n(n-1)+1.
Binomial transform of [1, 10, 10, 0, 0, 0,...]; Narayana transform (A001263) of [1, 10, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
a(n)=10*n+a(n-1)-10 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
G.f. -x*(1+8*x+x^2) / (x-1)^3 . - R. J. Mathar, Feb 04 2011
a(n) = A124080(n-1) + 1. - Omar E. Pol, Oct 03 2011
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EXAMPLE
| For n=2, a(2)=10*2+1-10=11; n=3, a(3)=10*3+11-10=31; n=4, a(4)=10*4+31-10=61 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MATHEMATICA
| lst={}; Do[p=(5*(n^2-n))+1; AppendTo[lst, p], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
FoldList[#1 + #2 &, 1, 10 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
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PROG
| (PARI) j=[]; for(n=1, 75, j=concat(j, (5*n*(n-1)+1))); j
(PARI) { for (n=1, 1000, write("b062786.txt", n, " ", 5*n*(n - 1) + 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 11 2009]
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CROSSREFS
| Cf. A001263.
Sequence in context: A113747 A202007 A125239 * A090562 A174244 A136061
Adjacent sequences: A062783 A062784 A062785 * A062787 A062788 A062789
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 19 2001
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EXTENSIONS
| Better description from Terry Trotter, Apr 06, 2002.
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