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A062786 Centered 10-gonal numbers. 15
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; text; internal format)
OFFSET

1,2

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, 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

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)

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, Dec 29 2007

a(n)=10*n+a(n-1)-10 (with a(1)=1) [From Vincenzo Librandi, 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

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, Aug 07 2010]

MATHEMATICA

lst={}; Do[p=(5*(n^2-n))+1; AppendTo[lst, p], {n, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Sep 27 2008]

FoldList[#1 + #2 &, 1, 10 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

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, Aug 11 2009]

CROSSREFS

Cf. A001263.

Sequence in context: A113747 A202007 A125239 * A090562 A174244 A136061

Adjacent sequences:  A062783 A062784 A062785 * A062787 A062788 A062789

KEYWORD

easy,nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jul 19 2001

EXTENSIONS

Better description from Terry Trotter, Apr 06, 2002.

STATUS

approved

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Last modified August 27 09:21 EDT 2014. Contains 246133 sequences.