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A140944 Triangle T(d,n) read by rows, the n-th term of the d-th differences of the Jacobsthal sequence A001045. 3
0, 1, 0, -1, 2, 0, 3, -2, 4, 0, -5, 6, -4, 8, 0, 11, -10, 12, -8, 16, 0, -21, 22, -20, 24, -16, 32, 0, 43, -42, 44, -40, 48, -32, 64, 0, -85, 86, -84, 88, -80, 96, -64, 128, 0, 171, -170, 172, -168, 176, -160, 192, -128, 256, 0, -341, 342, -340, 344, -336, 352, -320, 384, -256, 512, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A variant of the triangle A140503, now including the diagonal.

Since the diagonal contains zeros, rows sums are those of A140503.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(d,n)=T(d-1,n+1)-T(d-1,n). T(0,n)=A001045(n).

EXAMPLE

0;

1, 0;

-1, 2, 0;

3, -2, 4, 0;

-5, 6, -4, 8, 0;

11, -10, 12, -8, 16, 0;

-21, 22, -20, 24, -16, 32, 0;

MAPLE

A140944 := proc(d, n) if d = 0 then A001045(n) ; else procname(d-1, n+1)-procname(d-1, n) ; fi; end:

seq(seq(A140944(d, n), n=0..d), d=0..10) ; # R. J. Mathar, Sep 07 2009

MATHEMATICA

T[0, 0] = 0; T[1, 0] = T[0, 1] = 1; T[0, n_] := T[0, n] = T[0, n-1] + 2*T[0, n-2]; T[d_, d_]=0; T[d_, n_] := T[d, n] = T[d-1, n+1] - T[d-1, n]; Table[T[d, n], {d, 0, 10}, {n, 0, d}] // Flatten (* Jean-Fran├žois Alcover, Dec 17 2014 *)

CROSSREFS

Cf. A140503.

Sequence in context: A208435 A208457 A232343 * A057860 A092915 A063749

Adjacent sequences:  A140941 A140942 A140943 * A140945 A140946 A140947

KEYWORD

sign,tabl

AUTHOR

Paul Curtz, Jul 24 2008

EXTENSIONS

Edited and extended by R. J. Mathar, Sep 07 2009

STATUS

approved

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Last modified October 29 04:54 EDT 2020. Contains 338066 sequences. (Running on oeis4.)