

A062786


Centered 10gonal 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
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OFFSET

1,2


COMMENTS

Deleting the least significant digit yields the (n1)st triangular number: a(n) = 5n(n1)+1 = 10{n(n1)/2} +1 = 10*T(n1) +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(n1)+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(n1)10 (with a(1)=1) [From Vincenzo Librandi, Aug 07 2010]
G.f. x*(1+8*x+x^2) / (x1)^3 .  R. J. Mathar, Feb 04 2011
a(n) = A124080(n1) + 1.  Omar E. Pol, Oct 03 2011


EXAMPLE

For n=2, a(2)=10*2+110=11; n=3, a(3)=10*3+1110=31; n=4, a(4)=10*4+3110=61 [From Vincenzo Librandi, Aug 07 2010]


MATHEMATICA

lst={}; Do[p=(5*(n^2n))+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*(n1)+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



