1,6

This sequence can be used to help find an extension for A006209.

B.-S. Du, A simple method which generates infinitely many congruence indentities, Fib. Quart., 27 (1989), 116-124.

For i=2 and k >= 1 b(k+2, 2, n, n)=b(k, 2, 1, n) + b(k+1, 2, n, n). The remaining portion for the recurrence is defined in the reference.

E.g. for m = 5 and n = 2, b(5,2,2,2)= b(3,2,1,2) + b(4,2,2,2)= 2 because of the definition in the reference.

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

3 1 1 1 1 1 1 1 1 1 1 1 1 1 1

5 2 1 1 1 1 1 1 1 1 1 1 1 1 1

8 3 1 1 1 1 1 1 1 1 1 1 1 1 1

13 5 2 1 1 1 1 1 1 1 1 1 1 1 1

21 7 3 1 1 1 1 1 1 1 1 1 1 1 1

34 11 5 2 1 1 1 1 1 1 1 1 1 1 1

55 16 7 3 1 1 1 1 1 1 1 1 1 1 1

89 25 11 5 2 1 1 1 1 1 1 1 1 1 1

144 37 15 7 3 1 1 1 1 1 1 1 1 1 1

233 57 23 11 5 2 1 1 1 1 1 1 1 1 1

377 85 32 15 7 3 1 1 1 1 1 1 1 1 1

610 130 49 23 11 5 2 1 1 1 1 1 1 1 1

b := proc(k, i, j, n) option remember; if k = 1 then if i = 1 then return 0; end if; if i = 2 then if j = n then return 1; end if; return 0; end if; end if; if k = 2 then if i = 1 then return 1; end if; if i = 2 then if j = n then return 1; end if; return 0; end if; end if; if j = n then return b(k-2, i, 1, n) + b(k-1, i, n, n); end if; return b(k-2, i, 1, n) + b(k-2, i, j+1, n); end proc; (Deugau)

Cf. A006209.

Sequence in context: A107682 A085476 A124944 this_sequence A111946 A137844 A079229

Adjacent sequences: A094389 A094390 A094391 this_sequence A094393 A094394 A094395

nonn,tabl

Amy Robinson (amylou(AT)mchsi.com), Apr 28 2004

Corrected and extended by Chris Deugau (deugaucj(AT)uvic.ca), Dec 19 2005