A125003 a(0) = 0, a(1) = 5; for n>1, a(n) is determined by the rule that the concatenation of the leading terms of the difference triangle is the same as the concatenation of the digits of the sequence.

0, 5, 11, 19, 31, 59, 137, 337, 795, 1767, 3759, 7813, 16097, 33075, 67793, 138347, 280677, 566041, 1136129, 2274529, 4554047, 9143516, 18450225, 37464726, 76561127, 157278265, 324136399, 668557741, 1376893670, 2826272837

Offset

0,2

Comments

a(0) = 0, a(1) = 5; binomial transform of sequence gives successive digits of sequence.

Links

Table of n, a(n) for n=0..29.

N. J. A. Sloane, Transforms

Example

Triangle of successive differences begins:
0...5...11...19....31....59....137...337...795....
..5...6....8....12....28....78....200...458
....1....2....4....16....50....122...258
......1....2....12....34....72....136
.........1...10....22....38....64
...........9....12....16....26
..............3.....4....10
.................1.....6
....................5

Maple

revert := proc(n) local Linv, i, L ; L := convert(n, base, 10) ; Linv := [] ; for i from 1 to nops(L) do Linv := [op(Linv), op(-i, L)] ; od ; RETURN(Linv) ; end: A125003 := proc(nmax) local ldigs, T, diag, row ; T := array(1..nmax, 1..nmax) ; ldigs := [0, 5, 1, 1] ; T[1, 1] := ldigs[1] ; T[1, 2] := ldigs[2] ; T[2, 1] := ldigs[2] ; for diag from 3 to nmax do T[diag, 1] := ldigs[diag] ; for row from diag-1 to 1 by -1 do T[row, diag-row+1] := T[row, diag-row]+T[row+1, diag-row] ; od ; if diag > 3 then ldigs := [op(ldigs), op(revert(T[1, diag])) ] ; fi ; od ; RETURN(T) ; end : nmax := 50 : T := A125003(nmax) : for i from 1 to nmax do printf("%d, ", T[1, i]) ; od ; # R. J. Mathar, Jan 10 2007

Crossrefs

Cf. A125588, A125004, A125591.

Sequence in context: A079850 A065995 A023245 * A062718 A326123 A288112

Adjacent sequences: A125000 A125001 A125002 * A125004 A125005 A125006

Keyword

nonn,easy,base

Author

Eric Angelini, Jan 06 2007

Extensions

More terms from R. J. Mathar, Jan 10 2007

Status

approved