A109059 - OEIS

A109059

To compute a(n) we first write down 7^n 1's in a row. Each row takes the rightmost 7th part of the previous row and each element in it equals sum of the elements of the previous row starting with the first of the rightmost 7th part. The single element in the last row is a(n).

1, 1, 7, 322, 102249, 226742516, 3518406903403, 382149784071841422, 290546585470549214822793, 1546306129153609960601346281449, 57606719909341067627899562630623352149, 15022729501707009545842655841005666468590455864, 27423481304702360472157221630747597794702587610760693525

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

OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..49

EXAMPLE

For example, for n=3 the array, from 2nd row, follows:

1..2..3.....38..39..40..41..42..43..44..45..46..47..48..49

................................43..87.132.178.225.273.322

.......................................................322

Therefore a(3)=322.

MAPLE

proc(n::nonnegint) local f, a; if n=0 or n=1 then return 1; end if; f:=L->[seq(add(L[i], i=6*nops(L)/7+1..j), j=6*nops(L)/7+1..nops(L))]; a:=f([seq(1, j=1..7^n)]); while nops(a)>7 do a:=f(a) end do; a[7]; end proc;

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 1, -Sum[A[j, k]*(-1)^(n - j)* Binomial[If[j == 0, 1, k^j], n - j], {j, 0, n - 1}]];

a[n_] := A[n, 7];

Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Apr 01 2024, after_Alois P. Heinz_ in A355576 *)

CROSSREFS

Cf. A107354, A109055, A109056, A109057, A109058, A109060, A109061, A109062.

Column k=7 of A355576.

Sequence in context: A082160 A220278 A163437 * A002000 A374418 A092588

Adjacent sequences: A109056 A109057 A109058 * A109060 A109061 A109062

KEYWORD

nonn

AUTHOR

Augustine O. Munagi, Jun 17 2005

EXTENSIONS

More terms from Alois P. Heinz, Jul 06 2022

STATUS

approved