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A062786 Centered 10-gonal numbers. 16
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

a(n) = 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). - 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. - Vincenzo Librandi, Aug 07 2010

MATHEMATICA

lst={}; Do[p=(5*(n^2-n))+1; AppendTo[lst, p], {n, 5!}]; lst (* 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) ) } \\ 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,changed

AUTHOR

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

EXTENSIONS

Better description from Terrel Trotter, Jr., Apr 06 2002

STATUS

approved

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Last modified March 2 14:12 EST 2015. Contains 255132 sequences.