

A140090


a(n) = n*(3*n+7)/2.


30



0, 5, 13, 24, 38, 55, 75, 98, 124, 153, 185, 220, 258, 299, 343, 390, 440, 493, 549, 608, 670, 735, 803, 874, 948, 1025, 1105, 1188, 1274, 1363, 1455, 1550, 1648, 1749, 1853, 1960, 2070, 2183, 2299, 2418, 2540, 2665, 2793, 2924
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

This sequence is mentioned in the GuoNiu Han's paper, chapter 6: Dictionary of the standard puzzle sequences, p. 19 (see link).  Omar E. Pol, Oct 28 2011


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000
GuoNiu Han, Enumeration of Standard Puzzles [broken link]
GuoNiu Han, Enumeration of Standard Puzzles [Cached copy]
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x*(52*x)/(1x)^3.  Bruno Berselli, Feb 11 2011
a(n) = (3*n^2 + 7*n)/2.
a(n) = a(n1) + 3*n+2 (with a(0)=0).  Vincenzo Librandi, Nov 24 2010
E.g.f.: (1/2)*(3*x^2 + 10*x)*exp(x).  G. C. Greubel, Jul 17 2017


MATHEMATICA

s=1; lst={}; Do[s+=n+n+n1; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 04 2008 *)
Table[Sum[i + n  3, {i, 4, n}], {n, 3, 50}] (* Zerinvary Lajos, Jul 11 2009 *)


PROG

(PARI) a(n)=n*(3*n+7)/2 \\ Charles R Greathouse IV, Sep 24 2015


CROSSREFS

The generalized pentagonal numbers b*n+3*n*(n1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.
Cf. numbers of the form n*(d*n+10d)/2: A008587, A056000, A028347, A014106, A028895, A045944, A186029, A007742, A022267, A033429, A022268, A049452, A186030, A135703, A152734, A139273.
Sequence in context: A075829 A119248 A114998 * A271937 A121511 A283750
Adjacent sequences: A140087 A140088 A140089 * A140091 A140092 A140093


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, May 22 2008


STATUS

approved



