Search: id:A060544
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%I A060544
%S A060544 1,10,28,55,91,136,190,253,325,406,496,595,703,820,946,1081,1225,1378,
%T A060544 1540,1711,1891,2080,2278,2485,2701,2926,3160,3403,3655,3916,4186,4465,
%U A060544 4753,5050,5356,5671,5995,6328,6670,7021,7381,7750,8128,8515,8911,9316
%N A060544 Centered 9-gonal (or nonagonal) numbers. Every third triangular number, 
               starting with a(1)=1.
%C A060544 Triangular numbers not == 0 (mod 3). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Nov 13 2005
%C A060544 Shallow diagonal of triangular spiral in A051682. - Paul Barry (pbarry(AT)wit.ie), 
               Mar 15 2003
%C A060544 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]
%C A060544 Except for the first term, a(n)=9*n+a(n-1), (with a(1)=10) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
%H A060544 T. D. Noe, <a href="b060544.txt">Table of n, a(n) for n=1..1000</a>
%H A060544 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A060544 <a href="Sindx_Ce.html#CENTRALCUBE">Index entries for sequences related 
               to centered polygonal numbers</a>
%H A060544 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MarionsTheorem.html">Marion's Theorem</a> [From Eric W. Weisstein 
               (eric(AT)weisstein.com), Nov 23 2008]
%F A060544 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.(1+7x+x^2)/(1-x)^3. - Paul Barry 
               (pbarry(AT)wit.ie), Mar 15 2003
%F A060544 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).
%F A060544 G.f.: x(1+7x+x^2)/(1-x)^3. a(1-n)=a(n).
%F A060544 Binomial transform of [1, 9, 9, 0, 0, 0,...]; Narayana transform (A001263) 
               of [1, 9, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 29 2007
%F A060544 a(n)=9*n+a(n-1)-9 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 10 2009]
%e A060544 For n=2, a(2)=9*2+1-9=10; n=3, a(3)=9*3+10-9=28; n=4, a(4)=9*4+28-9=55 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 10 2009]
%t A060544 Transpose[Partition[Accumulate[Range[150]],3]][[1]] [From Harvey P. Dale 
               (hpd1(AT)nyu.edu), Nov 01 2009]
%o A060544 (PARI) a(n)=(3*n-1)*(3*n-2)/2
%o A060544 (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]
%Y A060544 Cf. A027468, A081266.
%Y A060544 Cf. A001263.
%Y A060544 Sequence in context: A113746 A117464 A081273 this_sequence A088406 A054112 
               A053790
%Y A060544 Adjacent sequences: A060541 A060542 A060543 this_sequence A060545 A060546 
               A060547
%K A060544 easy,nice,nonn,new
%O A060544 1,2
%A A060544 Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001
%E A060544 Additional description from Terry Trotter, Apr 06, 2002.

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