0,3

Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the line from 0 in the direction 0,1,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:

......15

....16..14

..17..3...13

18..4...2...12

..5...0...1...11

6...7...8...9...10

(1), (4+7), (7+10+13), (10+13+16+19), ... - Jon Perry (perry(AT)globalnet.co.uk), Sep 10 2004

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

n*(9*n-7)/2.

G.f.: x*(1+8*x)/(1-x)^3.

Row sums of triangle A131432 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 10 2007

a(n)=9*n+a(n-1)-17 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

For n=2, a(2)=9*2+0-17=1; n=3, a(3)=9*3+1-17=11; n=4, a(4)=9*4+11-17=30 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+9 od: seq(a[n], n=0..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 9}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]

First differences of A007586.

Cf. A001107, A000567.

Cf. A093644 ((9, 1) Pascal, column m=2). Partial sums of A017173.

Cf. A004188.

Cf. A131432.

Cf. A000217, A001107, A051624.

Sequence in context: A146751 A162734 A163060 this_sequence A109943 A137411 A002755

Adjacent sequences: A051679 A051680 A051681 this_sequence A051683 A051684 A051685

easy,nonn

Barry E. Williams

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999