OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = 2^n + k - 2, n>=1, k>=1.
EXAMPLE
Northwest corner:
1....2....3....4....5
3....4....5....6....7
7....8....9....10...11
15...16...17...18...19
31...32...33...34...35
MATHEMATICA
(* This program prints the array T=A185738, the accumulation array A185739 of T, and the weight array A185740 of T. *)
f[n_, 0]:=0; f[0, k_]:=0;
f[n_, k_]:=2^n+k-2;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* Array A185738 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)
FullSimplify[s[n, k]] (* formula for accumulation array *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* Array A185739 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
w[m_, n_]:=f[m, n]+f[m-1, n-1]-f[m, n-1]-f[m-1, n]/; Or[m>0, n>0];
TableForm[Table[w[n, k], {n, 1, 10}, {k, 1, 15}]] (* Array A185740 *)
Table[w[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 02 2011
STATUS
approved