A378704
Array read by ascending antidiagonals: A(n, k) is the total area of n-Fibonacci polyominoes with k columns, where k > 0.
Original entry on oeis.org
2, 3, 7, 4, 11, 16, 5, 15, 31, 35, 6, 19, 43, 73, 70, 7, 23, 55, 111, 168, 136, 8, 27, 67, 143, 261, 370, 256, 9, 31, 79, 175, 351, 602, 790, 473, 10, 35, 91, 207, 431, 816, 1350, 1658, 860, 11, 39, 103, 239, 511, 1023, 1865, 2966, 3425, 1545, 12, 43, 115, 271, 591, 1215, 2346, 4178, 6414, 6989, 2748
Offset: 2
The array begins as:
2, 7, 16, 35, 70, 136, 256, ...
3, 11, 31, 73, 168, 370, 790, ...
4, 15, 43, 111, 261, 602, 1350, ...
5, 19, 55, 143, 351, 816, 1865, ...
6, 23, 67, 175, 431, 1023, 2346, ...
7, 27, 79, 207, 511, 1215, 2815, ...
...
-
A[n_,k_]:=SeriesCoefficient[y(n^2(1-y)^2y^n+2y(1-y^n)-n(1-y)(2-y^n+y^(n+1)))/(2(-1+y)(1-2y+y^(n+1))^2),{y,0,k}]; Table[A[n-k+1,k],{n,2,12},{k,n-1}]//Flatten
A378706
Array read by ascending antidiagonals: A(n,k) is the total semi-perimeter of n-Fibonacci polyominoes with k columns, where k > 0.
Original entry on oeis.org
3, 4, 8, 5, 10, 16, 6, 12, 25, 33, 7, 14, 29, 54, 63, 8, 16, 33, 69, 118, 119, 9, 18, 37, 77, 152, 251, 219, 10, 20, 41, 85, 177, 335, 521, 398, 11, 22, 45, 93, 193, 390, 727, 1071, 714, 12, 24, 49, 101, 209, 433, 856, 1557, 2176, 1269, 13, 26, 53, 109, 225, 465, 948, 1859, 3297, 4380, 2237
Offset: 2
The array begins as:
3, 8, 16, 33, 63, 119, 219, 398, 714, 1269, ...
4, 10, 25, 54, 118, 251, 521, 1071, 2176, 4380, ...
5, 12, 29, 69, 152, 335, 727, 1557, 3297, 6931, ...
6, 14, 33, 77, 177, 390, 856, 1859, 4001, 8545, ...
7, 16, 37, 85, 193, 433, 948, 2065, 4463, 9581, ...
...
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A[n_, k_]:=SeriesCoefficient[(n(1-y)y(1-2y-2y^n+3y^(n+1))-y(1-y^n)(-1+y-y^2+y^(n+2)))/((1-y)(1-2y+y^(n+1))^2), {y, 0, k}]; Table[A[n-k+1, k], {n, 2, 12}, {k, n-1}]//Flatten
A378707
Array read by ascending antidiagonals: A(n,k) is the total number of inner points of n-Fibonacci polyominoes with k columns, where k > 0.
Original entry on oeis.org
0, 0, 1, 0, 3, 3, 0, 5, 10, 7, 0, 7, 18, 26, 15, 0, 9, 26, 50, 63, 30, 0, 11, 34, 74, 124, 143, 58, 0, 13, 42, 98, 190, 296, 313, 109, 0, 15, 50, 122, 254, 457, 679, 668, 201, 0, 17, 58, 146, 318, 622, 1070, 1517, 1398, 365, 0, 19, 66, 170, 382, 782, 1461, 2439, 3325, 2883, 655
Offset: 2
The array begins as:
0, 1, 3, 7, 15, 30, 58, 109, 201, 365, ...
0, 3, 10, 26, 63, 143, 313, 668, 1398, 2883, ...
0, 5, 18, 50, 124, 296, 679, 1517, 3325, 7184, ...
0, 7, 26, 74, 190, 457, 1070, 2439, 5453, 12013, ...
0, 9, 34, 98, 254, 622, 1461, 3361, 7583, 16857, ...
0, 11, 42, 122, 318, 782, 1854, 4272, 9681, 21615, ...
0, 13, 50, 146, 382, 942, 2238, 5182, 11754, 26302, ...
...
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A[n_, k_]:=SeriesCoefficient[y((6-4n)y-(2-4n)y^2-(3-n)n y^n-2(2-n)^2y^(n+1)+(2-5n+n^2)y^(n+2)+2y^(2n+1))/(2(-1+y)(1-2y+y^(n+1))^2), {y, 0, k}]; Table[A[n-k+1, k], {n, 2, 12}, {k, n-1}]//Flatten
Showing 1-3 of 3 results.