A268721 -id:A268721 - cp's OEIS frontend

A268724 Square array A(i,j) = A006068(i) * A006068(j), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 3, 3, 2, 9, 2, 7, 6, 6, 7, 6, 21, 4, 21, 6, 4, 18, 14, 14, 18, 4, 5, 12, 12, 49, 12, 12, 5, 15, 15, 8, 42, 42, 8, 15, 15, 14, 45, 10, 28, 36, 28, 10, 45, 14, 12, 42, 30, 35, 24, 24, 35, 30, 42, 12, 13, 36, 28, 105, 30, 16, 30, 105, 28, 36, 13, 8, 39, 24, 98, 90, 20, 20, 90, 98, 24, 39, 8, 9, 24, 26, 84, 84, 60, 25, 60, 84, 84, 26, 24, 9

Offset: 1

Antti Karttunen, Feb 13 2016

			The top left [1 .. 15] x [1 .. 15] section of the array:
   1,  3,  2,  7,   6,  4,  5,  15,  14,  12,  13,   8,   9,  11,  10
   3,  9,  6,  21, 18, 12, 15,  45,  42,  36,  39,  24,  27,  33,  30
   2,  6,  4,  14, 12,  8, 10,  30,  28,  24,  26,  16,  18,  22,  20
   7, 21, 14,  49, 42, 28, 35, 105,  98,  84,  91,  56,  63,  77,  70
   6, 18, 12,  42, 36, 24, 30,  90,  84,  72,  78,  48,  54,  66,  60
   4, 12,  8,  28, 24, 16, 20,  60,  56,  48,  52,  32,  36,  44,  40
   5, 15, 10,  35, 30, 20, 25,  75,  70,  60,  65,  40,  45,  55,  50
  15, 45, 30, 105, 90, 60, 75, 225, 210, 180, 195, 120, 135, 165, 150
  14, 42, 28,  98, 84, 56, 70, 210, 196, 168, 182, 112, 126, 154, 140
  12, 36, 24,  84, 72, 48, 60, 180, 168, 144, 156,  96, 108, 132, 120
  13, 39, 26,  91, 78, 52, 65, 195, 182, 156, 169, 104, 117, 143, 130
   8, 24, 16,  56, 48, 32, 40, 120, 112,  96, 104,  64,  72,  88,  80
   9, 27, 18,  63, 54, 36, 45, 135, 126, 108, 117,  72,  81,  99,  90
  11, 33, 22,  77, 66, 44, 55, 165, 154, 132, 143,  88,  99, 121, 110
  10, 30, 20,  70, 60, 40, 50, 150, 140, 120, 130,  80,  90, 110, 100

Antti Karttunen, Table of n, a(n) for n = 1..15051; the first 173 antidiagonals of the array

Cf. A268725.
Cf. A006068 (row 1, column 1).
Cf. A268716 (row 3, column 3).
Cf. A268721 (the antidiagonal sums).
Cf. also A268714.

(define (A268724 n) (A268724bi (A002260 n) (A004736 n)))
(define (A268724bi row col) (* (A006068 row) (A006068 col)))

A(i,j) = A006068(i) * A006068(j)

A(i,j) = A006068(A268725(i,j)).

A268836 Antidiagonal sums of array A268714: a(n) = Sum_{k=0..n} A006068(n)+A006068(n-k).

Original entry on oeis.org

0, 2, 8, 12, 26, 38, 46, 56, 86, 114, 138, 164, 180, 198, 220, 240, 302, 362, 418, 476, 524, 574, 628, 680, 712, 746, 784, 820, 866, 910, 950, 992, 1118, 1242, 1362, 1484, 1596, 1710, 1828, 1944, 2040, 2138, 2240, 2340, 2450, 2558, 2662, 2768, 2832, 2898, 2968, 3036, 3114, 3190, 3262, 3336, 3430, 3522, 3610, 3700

Offset: 0

Antti Karttunen, Feb 15 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..4096

Cf. A006068, A268714.
Cf. also A268837, A268721.
Partial sums of A268716.

(define (A268836 n) (add (lambda (k) (+ (A006068 k) (A006068 (- (+ n 0) k)))) 0 n))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

a(n) = Sum_{k=0..n} A006068(n)+A006068(n-k).

cp's OEIS Frontend

A268724 Square array A(i,j) = A006068(i) * A006068(j), read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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