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A185737 Accumulation array of the Wythoff array, by antidiagonals. 1
1, 3, 5, 6, 14, 11, 11, 28, 30, 20, 19, 51, 60, 54, 32, 32, 88, 109, 108, 86, 46, 53, 148, 188, 196, 172, 123, 63, 87, 245, 316, 338, 312, 246, 168, 82, 142, 402, 523, 568, 538, 446, 336, 218, 104, 231, 656, 858, 940, 904, 769, 609, 436, 276, 129, 375, 1067, 1400, 1542, 1496, 1292, 1050, 790, 552, 342, 156, 608, 1732, 2277, 2516, 2454, 2138, 1764, 1362, 1000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the definition of accumulation array, see A144112.

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

Northwest corner:

1....3....6....11....19  (A001911)

5....14...28...51....88

11...30...60...109...188

20...54...108..196...338

MATHEMATICA

(* This program creates the Wythoff array W={f(n, k)}=A035513, then the accumulation array A185736 of W, then the weight array A185736 of W *)

f[n_, 0]:=0; f[0, k_]:=0;  (* Needed for the weight array *)

f[n_, k_]:=Fibonacci[k+1]Floor[n*GoldenRatio]+(n-1)Fibonacci[k];

TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]  (* Wythoff array *)

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}];

TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185736 *)

Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

(* In general, the weight array W of an arbitrary rectangular array S={s(i, j):i<=1, j<=1} is defined in two steps:(1) define s(i, j)=0 if i=0 or j=0; (2) then w(m, n)=s(m, n)+s(m-1, n-1)-s(m, n-1)-s(m-1, n) for m1, n1. *)

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}]] (* A185736 *)

Table[w[n-k+1, k], {n, 20}, {k, n, 1, -1}]//Flatten

CROSSREFS

Cf. A144112, A035513, A185736.

Sequence in context: A285534 A064519 A048968 * A092862 A112863 A290964

Adjacent sequences:  A185734 A185735 A185736 * A185738 A185739 A185740

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 02 2011

STATUS

approved

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)