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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 13 22:16 EDT 2021. Contains 342941 sequences. (Running on oeis4.)