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A094392 Antidiagonals of the tables formed from b(m,2,n,n), which is defined in Du 1989. 7
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 8, 1, 1, 1, 1, 1, 3, 13, 1, 1, 1, 1, 1, 1, 5, 21, 1, 1, 1, 1, 1, 1, 2, 7, 34, 1, 1, 1, 1, 1, 1, 1, 3, 11, 55, 1, 1, 1, 1, 1, 1, 1, 1, 5, 16, 89, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 25, 144, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 37, 233, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..100.

Bau-Sen Du, A Simple Method Which Generates Infinitely Many Congruence Identities, Fib. Quart. 27 (1989), 116-124.

Bau-Sen Du, A Simple Method Which Generates Infinitely Many Congruence Identities, arXiv:0706.2421 [math.NT], 2007.

FORMULA

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 Du 1989.

EXAMPLE

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

MAPLE

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; # Chris Deugau (deugaucj(AT)uvic.ca), Dec 19 2005

MATHEMATICA

b[k_, i_, j_, n_] := b[k, i, j, n] = Which[k == 1, Which[i == 1, 0, i == 2 , If[j == n, 1, 0], True, 0], k == 2, Which[i == 1, 1, i == 2, If[j == n, 1, 0], True, 0], j == n, b[k - 2, i, 1, n] + b[k - 1, i, n, n], True, b[k - 2, i, 1, n] + b[k - 2, i, j + 1, n]];

a[m_, n_] := b[m, 2, n, n];

Table[a[m - n + 1, n], {m, 1, 14}, {n, m, 1, -1}] // Flatten (* Jean-François Alcover, Nov 21 2017, adapted from Maple *)

CROSSREFS

Cf. A006206 (A_{n,1}), A006207 (A_{n,2}), A006208 (A_{n,3}), A006209 (A_{n,4}), A130628 (A_{n,5}), A208092 (A_{n,6}), A006210 (D_{n,2}), A006211 (D_{n,3}), A094392.

Sequence in context: A260534 A085476 A124944 * A111946 A175788 A237513

Adjacent sequences:  A094389 A094390 A094391 * A094393 A094394 A094395

KEYWORD

nonn,tabl

AUTHOR

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

EXTENSIONS

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

Typo 891 -> 89,1 corrected by Jean-François Alcover, Nov 21 2017

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)