A225982 -id:A225982 - cp's OEIS frontend

A225976 Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

4, 15, 48, 138, 350, 790, 1616, 3049, 5384, 9001, 14376, 22092, 32850, 47480, 66952, 92387, 125068, 166451, 218176, 282078, 360198, 454794, 568352, 703597, 863504, 1051309, 1270520, 1524928, 1818618, 2155980, 2541720, 2980871, 3478804, 4041239

Offset: 1

R. H. Hardin, May 22 2013

nonn

			Some solutions for n=3:
..0..1....1..1....0..0....0..0....1..1....0..1....0..0....0..1....1..1....0..1
..0..0....1..1....1..1....0..1....1..0....0..1....0..1....0..1....0..0....0..1
..1..1....0..1....0..0....1..1....1..0....0..1....0..0....1..0....1..1....1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 2 of A225982.

Empirical: a(n) = (11/120)*n^5 - (1/8)*n^4 + (9/8)*n^3 - (7/8)*n^2 + (287/60)*n - 1.
Conjectures from Colin Barker, Sep 05 2018: (Start)
G.f.: x*(4 - 9*x + 18*x^2 - 5*x^3 + 2*x^4 + x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A225977 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

8, 48, 252, 1178, 4722, 16361, 49811, 135672, 336189, 768900, 1642668, 3310404, 6343682, 11635425, 20537903, 35044430, 58024377, 93522432, 147134436, 226473606, 341742522, 506427905, 738136947, 1059595772, 1499832509

Offset: 1

R. H. Hardin, May 22 2013

nonn

			Some solutions for n=3:
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..1....0..1..1
..1..0..0....0..1..0....1..1..1....1..0..1....0..1..0....0..1..0....0..0..1
..1..1..1....0..1..1....0..1..0....0..0..1....0..0..1....0..1..1....1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..101

Column 3 of A225982.

Empirical: a(n) = (1/4320)*n^9 + (23/6720)*n^8 + (5/336)*n^7 - (1/288)*n^6 + (659/1440)*n^5 + (443/2880)*n^4 + (80/27)*n^3 - (6203/1008)*n^2 + (2459/140)*n - 6 for n>1.
Conjectures from Colin Barker, Sep 05 2018: (Start)
G.f.: x*(8 - 32*x + 132*x^2 - 142*x^3 + 202*x^4 - 25*x^5 - 165*x^6 + 163*x^7 - 72*x^8 + 16*x^9 - x^10) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.
(End)

A225978 Number of nX4 binary arrays whose sum with another nX4 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

15, 138, 1178, 9113, 61808, 361361, 1825607, 8065278, 31631401, 111785599, 360788468, 1075829429, 2993017696, 7832960008, 19417916324, 45865067963, 103734768130, 225619306783, 473616394498, 962612525277, 1899542726132

Offset: 1

R. H. Hardin May 22 2013

nonn

Column 4 of A225982

			Some solutions for n=3
..0..0..0..1....0..0..1..1....0..0..1..1....0..0..0..1....0..0..0..1
..0..1..0..1....0..0..0..0....1..0..0..0....1..1..1..0....0..0..0..1
..1..0..1..1....1..0..0..1....0..0..0..1....0..1..0..0....1..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..76

Empirical: a(n) = (23/14820309504000)*n^17 + (397/2615348736000)*n^16 + (1429/217945728000)*n^15 + (21083/130767436800)*n^14 + (156407/62270208000)*n^13 + (375707/14370048000)*n^12 + (3136061/16765056000)*n^11 + (21563/22861440)*n^10 + (26402329/6096384000)*n^9 + (423919927/18289152000)*n^8 + (68634593/598752000)*n^7 + (144700261/1437004800)*n^6 + (19312991563/12108096000)*n^5 - (22496273857/4540536000)*n^4 + (97668459683/3027024000)*n^3 - (41460631/700700)*n^2 + (20134601/291720)*n - 23 for n>2

A225979 Number of nX5 binary arrays whose sum with another nX5 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

26, 350, 4722, 61808, 737893, 7718077, 69784592, 546720823, 3748375290, 22776885553, 124247348589, 615678539423, 2800456394451, 11798875157732, 46405595059222, 171524109659874, 599254527583339, 1988834906193438

Offset: 1

R. H. Hardin May 22 2013

nonn

Column 5 of A225982

			Some solutions for n=3
..0..0..1..1..1....0..0..0..1..0....0..0..1..1..1....1..1..1..1..0
..0..0..0..0..0....1..1..1..1..1....0..0..0..1..1....0..1..1..1..1
..1..0..0..0..0....1..1..0..1..1....1..0..1..1..1....1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..58
R. H. Hardin, Empirical polynomial of degree 33

Empirical polynomial of degree 33 (see link above)

A225980 Number of nX6 binary arrays whose sum with another nX6 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

42, 790, 16361, 361361, 7718077, 148890101, 2513743785, 36836074434, 470279869497, 5279223820491, 52686610737385, 472630223607623, 3849896640784837, 28735919289705656, 198113452132002555

Offset: 1

R. H. Hardin May 22 2013

nonn

Column 6 of A225982

			Some solutions for n=3
..0..0..1..1..1..1....0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..1..1..1
..1..0..0..0..0..1....0..1..0..0..1..0....0..1..0..0..0..0....0..0..0..0..0..1
..1..0..1..0..1..0....1..0..1..1..1..1....1..0..0..0..1..1....0..1..0..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..29

A225981 Number of nX7 binary arrays whose sum with another nX7 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

64, 1616, 49811, 1825607, 69784592, 2513743785, 80901937149, 2279339811483, 56056577764123, 1210023577040820, 23129995837890549, 395389054254892996, 6101927873439814335, 85761387564101647001

Offset: 1

R. H. Hardin May 22 2013

nonn

Column 7 of A225982

			Some solutions for n=3
..0..0..1..1..0..1..1....0..0..0..1..1..1..1....0..0..1..1..1..1..1
..1..0..0..0..1..1..1....0..1..0..0..0..0..0....0..0..1..1..1..0..1
..1..1..0..0..1..1..1....1..1..0..0..0..1..0....1..1..0..1..1..0..1

cp's OEIS Frontend

A225976 Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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A225977 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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A225978 Number of nX4 binary arrays whose sum with another nX4 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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A225979 Number of nX5 binary arrays whose sum with another nX5 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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A225980 Number of nX6 binary arrays whose sum with another nX6 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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A225981 Number of nX7 binary arrays whose sum with another nX7 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

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