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A064999 Partial sums of sequence (essentially A002378): 1, 2, 6, 12, 20, 30, 42, 56, 72, 90, ... 7
1, 3, 9, 21, 41, 71, 113, 169, 241, 331, 441, 573, 729, 911, 1121, 1361, 1633, 1939, 2281, 2661, 3081, 3543, 4049, 4601, 5201, 5851, 6553, 7309, 8121, 8991, 9921, 10913, 11969, 13091, 14281, 15541, 16873, 18279, 19761, 21321, 22961, 24683 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals triangle A144328 * [1, 2, 3, ...]. - Gary W. Adamson, Sep 18 2008

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Franck Ramaharo, Enumerating the states of the twist knot, arXiv:1712.06543 [math.CO], 2017.

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = A007290(n+2) + 1 = (n^3 + 3*n^2 + 2*n + 3)/3.

a(0) = 1, a(n) = n*(n+1) + a(n-1) for n > 1. - Gerald McGarvey, Sep 26 2004

O.g.f.: (1 - x + 3x^2 - x^3)/(1 - x)^4.

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^2-n od: seq(a[n], n=0..42); # Zerinvary Lajos, Jun 05 2008

MATHEMATICA

Table[(x^3 - x + 3)/3, {x, 1, 100}] (* Artur Jasinski, Feb 14 2007 *)

LinearRecurrence[{4, -6, 4, -1}, {1, 3, 9, 21}, 50] (* Vincenzo Librandi, Feb 28 2016 *)

PROG

(PARI) { for (n=0, 1000, if (n, a+=n*(n + 1), a=1); write("b064999.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009

(PARI) a(n) = (n^3+3*n^2+2*n+3)/3; \\ Altug Alkan, May 16 2018

(MAGMA) [(n^3+3*n^2+2*n+3)/3: n in [0..50]]; // Vincenzo Librandi, Feb 28 2016

CROSSREFS

Cf. A002378, A007290.

Cf. A144328. - Gary W. Adamson, Sep 18 2008

Sequence in context: A007518 A029494 A059774 * A100135 A024173 A097119

Adjacent sequences:  A064996 A064997 A064998 * A065000 A065001 A065002

KEYWORD

easy,nonn

AUTHOR

Klaus E. Kastberg (kastberg(AT)hotkey.net.au), Oct 31 2001

EXTENSIONS

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Nov 12 2001

STATUS

approved

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Last modified December 15 13:27 EST 2018. Contains 318149 sequences. (Running on oeis4.)