A276934 -id:A276934 - cp's OEIS frontend

A276616 Square array A(n,k) = A276953(n,k)/n!, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 3, 1, 4, 4, 1, 5, 6, 5, 1, 7, 7, 8, 6, 1, 9, 13, 9, 10, 7, 1, 10, 16, 21, 11, 12, 8, 1, 11, 18, 25, 31, 13, 14, 9, 1, 13, 19, 28, 36, 43, 15, 16, 10, 1, 15, 25, 29, 40, 49, 57, 17, 18, 11, 1, 16, 28, 41, 41, 54, 64, 73, 19, 20, 12, 1, 17, 30, 45, 61, 55, 70, 81, 91, 21, 22, 13, 1, 18, 31, 48, 66, 85, 71, 88, 100, 111, 23, 24, 14, 1

Offset: 1

Antti Karttunen, Sep 22 2016

			The top left corner of the array:
  1, 3,  4,  5,  7,  9, 10, 11,  13,  15,  16,  17,  18,  19,  20,  21,  22
  1, 4,  6,  7, 13, 16, 18, 19,  25,  28,  30,  31,  36,  37,  39,  40,  42
  1, 5,  8,  9, 21, 25, 28, 29,  41,  45,  48,  49,  60,  61,  64,  65,  68
  1, 6, 10, 11, 31, 36, 40, 41,  61,  66,  70,  71,  90,  91,  95,  96, 100
  1, 7, 12, 13, 43, 49, 54, 55,  85,  91,  96,  97, 126, 127, 132, 133, 138
  1, 8, 14, 15, 57, 64, 70, 71, 113, 120, 126, 127, 168, 169, 175, 176, 182

Transpose: A276617.
Cf. A000142, A276953.
Row 1: A273670, row 2: A276931, row 3: A276934.
For columns, see the rows of transpose A276617.

(define (A276616 n) (A276616bi (A002260 n) (A004736 n)))
(define (A276616bi row col) (/ (A276953bi row col) (A000142 row)))

A(n,k) = A276953(n,k)/n!

A276617 Square array A(n,k) = A276955(n,k)/k!, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 1, 3, 1, 4, 4, 1, 5, 6, 5, 1, 6, 8, 7, 7, 1, 7, 10, 9, 13, 9, 1, 8, 12, 11, 21, 16, 10, 1, 9, 14, 13, 31, 25, 18, 11, 1, 10, 16, 15, 43, 36, 28, 19, 13, 1, 11, 18, 17, 57, 49, 40, 29, 25, 15, 1, 12, 20, 19, 73, 64, 54, 41, 41, 28, 16, 1, 13, 22, 21, 91, 81, 70, 55, 61, 45, 30, 17, 1, 14, 24, 23, 111, 100, 88, 71, 85, 66, 48, 31, 18

Offset: 1

Antti Karttunen, Sep 22 2016

			The top left corner of the array:
1,  1,  1,  1,  1,  1,  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1
3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  13,  14,  15,  16,  17,  18,  19
4,  6,  8, 10, 12, 14, 16,  18,  20,  22,  24,  26,  28,  30,  32,  34,  36
5,  7,  9, 11, 13, 15, 17,  19,  21,  23,  25,  27,  29,  31,  33,  35,  37
7, 13, 21, 31, 43, 57, 73,  91, 111, 133, 157, 183, 211, 241, 273, 307, 343
9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361

Transpose: A276616.
Cf. A000142, A276955.
Columns 1-3: A273670, A276931, A276934.
Row 1: A000012, Row 2: n+2, Row 3: 2n+2, Row 4: 2n+3 (for n >= 1).
Row 5: A002061 (from a(3)=7 onward).
Row 6: squares (A000290, from a(3)=9 onward).
Row 7: A028552 (from a(2)=10 onward).
Row 8: A028387 (from a(2)=11 onward).

(define (A276617 n) (A276617bi (A002260 n) (A004736 n)))
(define (A276617bi row col) (/ (A276955bi row col) (A000142 col)))

A(n,k) = A276955(n,k)/k!

A276931 Row 2 of A276616: a(n) = A276932(n)/2.

Original entry on oeis.org

1, 4, 6, 7, 13, 16, 18, 19, 25, 28, 30, 31, 36, 37, 39, 40, 42, 43, 61, 64, 66, 67, 73, 76, 78, 79, 85, 88, 90, 91, 96, 97, 99, 100, 102, 103, 121, 124, 126, 127, 133, 136, 138, 139, 145, 148, 150, 151, 156, 157, 159, 160, 162, 163, 181, 184, 186, 187, 193, 196, 198, 199, 205, 208, 210, 211, 216, 217, 219, 220, 222

Offset: 0

Antti Karttunen, Sep 22 2016

Starting offset is 0 (with a(0) = 1) to match with the starting offset of A276932 and A273670.

Antti Karttunen, Table of n, a(n) for n = 0..10000
Index entries for sequences related to factorial base representation

Cf. A276932, A276934.

Row 2 of A276616, column 2 of A276617.

a(n) = A276932(n)/2.

A276933 Row 3 of A276953: a(n) = A153880(A153880(A273670(n))).

Original entry on oeis.org

6, 30, 48, 54, 126, 150, 168, 174, 246, 270, 288, 294, 360, 366, 384, 390, 408, 414, 726, 750, 768, 774, 846, 870, 888, 894, 966, 990, 1008, 1014, 1080, 1086, 1104, 1110, 1128, 1134, 1446, 1470, 1488, 1494, 1566, 1590, 1608, 1614, 1686, 1710, 1728, 1734, 1800, 1806, 1824, 1830, 1848, 1854, 2166, 2190, 2208, 2214, 2286, 2310

Offset: 0

Antti Karttunen, Sep 23 2016

All terms are multiples of 6. See A276934.

Antti Karttunen, Table of n, a(n) for n = 0..10000

Row 3 of A276953, column 3 of A276955.
Cf. A153880, A273670, A276932, A276934 (terms divided by six).
Indices of 3's in A276949.

(define (A276933 n) (A153880 (A153880 (A273670 n))))

a(n) = A153880(A153880(A273670(n))) = A153880(A276932(n)).

a(n) = 6*A276934(n).

cp's OEIS Frontend

A276616 Square array A(n,k) = A276953(n,k)/n!, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A276617 Square array A(n,k) = A276955(n,k)/k!, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A276931 Row 2 of A276616: a(n) = A276932(n)/2.

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A276933 Row 3 of A276953: a(n) = A153880(A153880(A273670(n))).

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