A247533 -id:A247533 - cp's OEIS frontend

A247527 Number of length n+3 0..2 arrays with some disjoint pairs in every consecutive four terms having the same sum.

33, 45, 61, 81, 105, 153, 217, 297, 393, 585, 841, 1161, 1545, 2313, 3337, 4617, 6153, 9225, 13321, 18441, 24585, 36873, 53257, 73737, 98313, 147465, 213001, 294921, 393225, 589833, 851977, 1179657, 1572873, 2359305, 3407881, 4718601, 6291465

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

			Some solutions for n=6:
..2....1....0....2....0....2....0....0....1....1....0....0....2....1....1....2
..1....0....1....1....1....1....1....1....0....1....2....0....1....2....2....1
..0....2....0....0....0....1....1....1....2....0....1....1....1....0....2....1
..1....1....1....1....1....0....0....0....1....2....1....1....2....1....1....2
..2....1....2....2....2....2....0....0....1....1....2....2....0....1....1....0
..1....0....1....1....1....1....1....1....2....1....2....2....1....2....0....1
..2....2....2....0....2....1....1....1....0....2....1....1....1....0....2....1
..1....1....1....1....1....0....0....0....1....2....1....1....2....1....1....0
..2....1....0....0....2....2....2....0....1....1....0....0....0....1....1....2

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

Column 2 of A247533.

Empirical: a(n) = a(n-1) + 4*a(n-4) - 4*a(n-5).

Empirical g.f.: x*(33 + 12*x + 16*x^2 + 20*x^3 - 108*x^4) / ((1 - x)*(1 - 2*x^2)*(1 + 2*x^2)). - Colin Barker, Nov 07 2018

A247528 Number of length n+3 0..3 arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

88, 136, 220, 364, 604, 1018, 1732, 2956, 5050, 8638, 14794, 25348, 43438, 74446, 127606, 218740, 374968, 642784, 1101898, 1888954, 3238192, 5551168, 9516268, 16313584, 27966124, 47941900, 82186078, 140890372, 241526284, 414044950

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

			Some solutions for n=6:
..2....0....2....0....0....2....3....3....2....2....0....1....3....3....0....2
..3....1....0....1....1....3....2....2....1....1....1....1....0....3....1....1
..1....3....1....1....3....1....2....1....2....1....0....0....0....2....1....0
..0....2....3....2....2....2....1....2....3....2....1....2....3....2....2....3
..2....2....2....2....0....0....1....1....2....2....2....1....3....1....0....2
..1....1....0....1....1....1....2....2....1....1....1....3....0....3....1....1
..1....1....1....3....1....1....0....1....2....3....2....0....0....2....1....2
..0....0....1....0....0....2....1....0....3....0....1....2....3....2....2....3
..2....2....2....2....0....2....3....1....2....2....2....1....3....3....0....0

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

Column 3 of A247533.

Empirical: a(n) = 2*a(n-1) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).

Empirical g.f.: 2*x*(44 - 20*x - 26*x^2 + 6*x^3 - 38*x^4 - 9*x^5 + 32*x^6) / ((1 - x)*(1 - x - x^2 - x^4 + x^6)). - Colin Barker, Nov 07 2018

A247529 Number of length n+3 0..4 arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

185, 317, 561, 1007, 1823, 3455, 6495, 12105, 22459, 43255, 82157, 154279, 287847, 556213, 1059205, 1992823, 3723991, 7202379, 13726813, 25838725, 48308217, 93456427, 178172281, 335410643, 627185919, 1213463869, 2313820457, 4355601755

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Column 4 of A247533

			Some solutions for n=6
..0....3....0....1....4....3....4....3....1....3....0....1....3....2....4....0
..1....4....4....2....1....2....2....4....0....2....3....0....0....4....1....0
..3....0....1....0....2....1....1....1....2....4....1....2....4....1....0....2
..4....1....3....1....3....2....3....0....3....1....2....1....1....3....3....2
..2....3....2....1....4....3....2....3....1....3....2....1....3....0....2....4
..1....4....2....2....1....4....2....2....2....0....3....2....2....2....1....0
..3....2....1....2....2....1....3....1....2....2....1....0....2....1....2....2
..2....3....1....1....3....0....1....2....3....1....0....3....3....1....3....2
..4....3....0....3....4....3....4....1....1....1....4....1....1....0....4....0

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

Empirical: a(n) = a(n-1) +4*a(n-2) -4*a(n-3) +18*a(n-4) -18*a(n-5) -78*a(n-6) +78*a(n-7) -67*a(n-8) +67*a(n-9) +386*a(n-10) -386*a(n-11) +22*a(n-12) -22*a(n-13) -686*a(n-14) +686*a(n-15) +125*a(n-16) -125*a(n-17) +616*a(n-18) -616*a(n-19) -178*a(n-20) +178*a(n-21) -340*a(n-22) +340*a(n-23) +130*a(n-24) -130*a(n-25) +80*a(n-26) -80*a(n-27) -40*a(n-28) +40*a(n-29) for n>30

A247530 Number of length n+3 0..5 arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

336, 600, 1124, 2164, 4228, 8440, 16932, 34068, 68688, 139040, 281646, 570720, 1157028, 2347720, 4764538, 9669762, 19627304, 39846710, 80899690, 164248362, 333480544, 677107822, 1374849942, 2791574878, 5668275372, 11509431434

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Column 5 of A247533

			Some solutions for n=6
..4....3....3....5....1....1....0....1....3....2....3....3....3....4....0....1
..2....2....2....4....4....4....4....3....2....2....4....4....2....3....2....0
..3....5....2....1....0....2....1....2....4....3....4....5....0....0....4....2
..3....4....1....2....5....3....5....0....3....1....5....4....5....1....2....1
..2....3....1....5....1....3....0....1....3....4....3....3....3....2....0....3
..4....2....0....4....4....2....4....1....4....2....2....2....2....1....2....4
..1....1....2....1....2....2....1....0....2....3....4....1....0....2....4....2
..3....4....3....0....5....3....3....2....5....5....1....4....1....1....2....1
..0....3....5....5....1....3....2....1....1....0....5....3....3....0....0....5

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

Empirical: a(n) = 2*a(n-1) +8*a(n-2) -17*a(n-3) +a(n-4) +10*a(n-5) -157*a(n-6) +279*a(n-7) +287*a(n-8) -676*a(n-9) +1052*a(n-10) -1443*a(n-11) -3411*a(n-12) +6586*a(n-13) -1985*a(n-14) +16*a(n-15) +16530*a(n-16) -27897*a(n-17) -7486*a(n-18) +26143*a(n-19) -37856*a(n-20) +52993*a(n-21) +39856*a(n-22) -98023*a(n-23) +38862*a(n-24) -20108*a(n-25) -65879*a(n-26) +144966*a(n-27) -16963*a(n-28) -66316*a(n-29) +54163*a(n-30) -75893*a(n-31) +4252*a(n-32) +70664*a(n-33) -27769*a(n-34) +2220*a(n-35) -2909*a(n-36) -15058*a(n-37) +10538*a(n-38) -826*a(n-39) +1788*a(n-40) +1646*a(n-41) -2884*a(n-42) +1344*a(n-43) -572*a(n-44) -615*a(n-45) +437*a(n-46) +140*a(n-47) +112*a(n-48) -190*a(n-49) -20*a(n-50) +78*a(n-51) +a(n-52) -24*a(n-53) +8*a(n-55) -4*a(n-56)

A247531 Number of length n+3 0..6 arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

553, 1033, 2009, 3997, 8051, 16683, 34695, 72269, 150677, 318575, 671847, 1413661, 2970293, 6314241, 13372035, 28225763, 59454011, 126633283, 268599173, 567619549, 1196758327, 2551010159, 5414437825, 11447235523, 24144688307

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Column 6 of A247533

			Some solutions for n=6
..6....4....4....3....4....1....4....4....2....2....6....4....0....5....6....6
..4....6....5....3....3....2....6....3....2....0....5....3....3....1....0....1
..5....1....6....4....3....1....5....6....3....3....4....3....2....4....4....4
..3....3....5....4....2....2....5....1....1....5....5....4....1....2....2....3
..2....4....6....3....4....3....4....4....4....2....4....4....2....3....6....0
..4....6....5....5....5....0....4....3....2....6....5....3....3....5....4....1
..3....5....4....4....3....1....3....2....5....1....4....3....2....6....4....2
..3....5....3....4....4....4....3....5....3....5....3....2....1....2....2....3
..2....4....4....3....2....3....2....4....4....0....2....2....4....3....2....2

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 82

Empirical recurrence of order 82 (see link above)

A247532 Number of length n+3 0..7 arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

848, 1616, 3220, 6584, 13668, 29012, 62108, 133716, 288996, 627654, 1366118, 2978172, 6500008, 14206554, 31071490, 67992670, 148845278, 325994076, 714155690, 1564780972, 3429103460, 7515830880, 16474726804, 36114808462

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Column 7 of A247533

			Some solutions for n=6
..6....1....2....6....4....5....5....4....0....1....2....4....3....5....1....4
..7....6....5....4....5....6....6....1....5....2....5....6....5....3....6....4
..3....4....7....5....6....2....5....5....4....1....6....5....6....4....3....5
..2....3....4....5....7....3....6....2....1....2....3....7....4....2....4....5
..6....1....2....4....4....5....5....6....0....3....4....4....7....1....5....4
..7....0....5....6....5....6....4....1....5....4....5....6....5....3....6....6
..3....4....1....5....2....2....5....5....4....3....2....5....6....4....7....5
..2....3....4....3....7....1....6....2....1....4....3....7....6....6....4....7
..6....1....2....4....4....7....7....4....0....3....6....6....7....5....5....4

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

A247534 Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

8, 45, 136, 317, 600, 1033, 1616, 2409, 3400, 4661, 6168, 8005, 10136, 12657, 15520, 18833, 22536, 26749, 31400, 36621, 42328, 48665, 55536, 63097, 71240, 80133, 89656, 99989, 111000, 122881, 135488, 149025, 163336, 178637, 194760, 211933, 229976

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

			Some solutions for n=6:
..4....0....4....5....6....4....3....3....0....4....3....0....6....5....3....0
..3....4....4....4....1....2....0....2....5....4....5....1....3....4....1....2
..3....6....3....2....4....3....3....4....1....5....5....3....2....6....4....0
..4....2....3....3....3....3....0....3....6....5....3....4....5....5....6....2
..4....4....4....3....6....4....3....1....2....6....3....6....0....5....3....0

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

Row 2 of A247533.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Also as a cubic plus a linear quasipolynomial with period 2:
Empirical for n mod 2 = 0: a(n) = (9/2)*n^3 + (3/2)*n^2 + 1*n + 1
Empirical for n mod 2 = 1: a(n) = (9/2)*n^3 + (3/2)*n^2 - (1/2)*n + (5/2).
Empirical g.f.: x*(8 + 29*x + 38*x^2 + 32*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 07 2018

A247535 Number of length 3+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

8, 61, 220, 561, 1124, 2009, 3220, 4901, 7016, 9737, 13000, 17025, 21688, 27245, 33572, 40929, 49140, 58553, 68924, 80613, 93400, 107641, 123056, 140113, 158440, 178509, 200012, 223393, 248260, 275209, 303748, 334453, 366920, 401689, 438264

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

			Some solutions for n=6:
..2....1....1....3....5....1....1....3....5....3....3....5....6....2....3....4
..2....5....4....4....5....0....3....0....4....1....2....6....4....5....2....2
..0....3....5....2....6....5....5....3....2....3....0....4....3....1....1....3
..4....3....2....3....4....6....3....6....3....5....1....5....1....4....2....3
..2....5....3....1....5....1....5....3....3....3....3....3....2....2....1....2
..6....5....6....2....5....0....3....6....2....5....4....4....0....5....0....4

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

Row 3 of A247533.

Empirical: a(n) = a(n-2) + 2*a(n-3) + a(n-4) - 2*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) + 2*a(n-9) + a(n-10) - a(n-12).
Also as a cubic plus a linear quasipolynomial with period 12:
Empirical for n mod 12 = 0: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n + 1
Empirical for n mod 12 = 1: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (385/54)
Empirical for n mod 12 = 2: a(n) = (563/54)*n^3 - (127/18)*n^2 + (10/9)*n + (97/27)
Empirical for n mod 12 = 3: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (19/2)
Empirical for n mod 12 = 4: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - (37/27)
Empirical for n mod 12 = 5: a(n) = (563/54)*n^3 - (127/18)*n^2 - (61/18)*n + (761/54)
Empirical for n mod 12 = 6: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - 1
Empirical for n mod 12 = 7: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (385/54)
Empirical for n mod 12 = 8: a(n) = (563/54)*n^3 - (127/18)*n^2 + (10/9)*n + (151/27)
Empirical for n mod 12 = 9: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (19/2)
Empirical for n mod 12 = 10: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - (91/27)
Empirical for n mod 12 = 11: a(n) = (563/54)*n^3 - (127/18)*n^2 - (61/18)*n + (761/54).
Empirical g.f.: x*(8 + 61*x + 212*x^2 + 484*x^3 + 774*x^4 + 963*x^5 + 892*x^6 + 661*x^7 + 330*x^8 + 120*x^9 - x^11) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 07 2018

A247536 Number of length 4+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

8, 81, 364, 1007, 2164, 3997, 6584, 10219, 14852, 20847, 28108, 37095, 47564, 60087, 74428, 91101, 109760, 131243, 154956, 181677, 211024, 243709, 279136, 318445, 360676, 406933, 456648, 510683, 568172, 630613, 696744, 767859, 843244, 923955

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Row 4 of A247533

			Some solutions for n=6
..2....1....3....6....3....3....2....0....4....5....5....0....2....4....5....1
..0....0....5....3....5....6....4....2....3....6....1....2....0....0....4....5
..4....3....3....0....2....2....3....4....2....3....4....1....2....3....5....0
..2....2....5....3....6....5....5....2....5....2....2....3....4....1....6....6
..2....1....3....0....3....3....4....0....4....5....5....2....2....2....5....1
..0....4....5....3....5....4....6....2....1....0....1....0....4....0....4....5
..0....5....3....0....2....2....3....4....0....3....4....1....2....3....3....2

R. H. Hardin, Table of n, a(n) for n = 1..349

Empirical: a(n) = -a(n-1) -a(n-2) +a(n-4) +2*a(n-5) +3*a(n-6) +3*a(n-7) +2*a(n-8) -2*a(n-10) -4*a(n-11) -4*a(n-12) -4*a(n-13) -2*a(n-14) +2*a(n-16) +3*a(n-17) +3*a(n-18) +2*a(n-19) +a(n-20) -a(n-22) -a(n-23) -a(n-24)
Also as a cubic plus a linear quasipolynomial with period 420, first 12 listed:
Empirical for n mod 420 = 0: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n + 1
Empirical for n mod 420 = 1: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (622/45)
Empirical for n mod 420 = 2: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (3263/210)*n + (3998/315)
Empirical for n mod 420 = 3: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (148/5)
Empirical for n mod 420 = 4: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (3821/315)
Empirical for n mod 420 = 5: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (341/70)*n + (3580/63)
Empirical for n mod 420 = 6: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (404/35)
Empirical for n mod 420 = 7: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (784/45)
Empirical for n mod 420 = 8: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (3263/210)*n + (1187/45)
Empirical for n mod 420 = 9: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (886/35)
Empirical for n mod 420 = 10: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (184/9)
Empirical for n mod 420 = 11: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (341/70)*n + (20294/315)

A247537 Number of length 5+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

Original entry on oeis.org

8, 105, 604, 1823, 4228, 8051, 13668, 21609, 31924, 45309, 61740, 82067, 105968, 134635, 167680, 206001, 249072, 298861, 354032, 416027, 484464, 560643, 643428, 735401, 834308, 942581, 1059436, 1186239, 1321332, 1468271, 1624036, 1791277

Offset: 1

R. H. Hardin, Sep 18 2014

nonn

Row 5 of A247533

			Some solutions for n=6
..3....6....4....4....3....2....5....5....4....1....3....2....5....2....5....6
..1....2....2....3....2....1....6....4....0....2....2....6....6....2....4....4
..2....1....3....4....4....5....0....6....6....5....4....3....3....1....4....5
..0....5....1....3....1....6....1....5....2....4....3....5....2....1....5....3
..1....4....0....2....5....2....5....5....4....3....3....2....5....0....3....4
..3....0....4....1....0....1....4....4....0....6....2....4....6....2....4....2
..4....1....5....0....4....5....2....4....6....5....4....3....1....3....4....3
..6....5....1....3....1....6....3....5....2....2....3....1....0....5....3....3

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

Empirical: a(n) = -3*a(n-1) -6*a(n-2) -10*a(n-3) -15*a(n-4) -19*a(n-5) -21*a(n-6) -20*a(n-7) -15*a(n-8) -5*a(n-9) +9*a(n-10) +26*a(n-11) +44*a(n-12) +60*a(n-13) +71*a(n-14) +75*a(n-15) +70*a(n-16) +55*a(n-17) +32*a(n-18) +3*a(n-19) -29*a(n-20) -60*a(n-21) -85*a(n-22) -102*a(n-23) -108*a(n-24) -102*a(n-25) -85*a(n-26) -60*a(n-27) -29*a(n-28) +3*a(n-29) +32*a(n-30) +55*a(n-31) +70*a(n-32) +75*a(n-33) +71*a(n-34) +60*a(n-35) +44*a(n-36) +26*a(n-37) +9*a(n-38) -5*a(n-39) -15*a(n-40) -20*a(n-41) -21*a(n-42) -19*a(n-43) -15*a(n-44) -10*a(n-45) -6*a(n-46) -3*a(n-47) -a(n-48)
Also as a cubic plus a linear quasipolynomial with period 27720, first 12 listed:
Empirical for n mod 27720 = 0: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (878029/6930)*n + 1
Empirical for n mod 27720 = 1: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3587189/34650)*n - (44311/13860)
Empirical for n mod 27720 = 2: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (420821/3850)*n + (45853/2475)
Empirical for n mod 27720 = 3: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (716329/6930)*n + (17263/300)
Empirical for n mod 27720 = 4: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (4379057/34650)*n - (891203/17325)
Empirical for n mod 27720 = 5: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (198223/2310)*n + (44759/252)
Empirical for n mod 27720 = 6: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (4395689/34650)*n - (68743/1155)
Empirical for n mod 27720 = 7: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3587189/34650)*n + (341887/9900)
Empirical for n mod 27720 = 8: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (84041/770)*n + (1394257/17325)
Empirical for n mod 27720 = 9: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3570557/34650)*n + (56851/1100)
Empirical for n mod 27720 = 10: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (878029/6930)*n - (9023/99)
Empirical for n mod 27720 = 11: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (992963/11550)*n + (275239/1260)

cp's OEIS Frontend

A247527 Number of length n+3 0..2 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247528 Number of length n+3 0..3 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247529 Number of length n+3 0..4 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247530 Number of length n+3 0..5 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247531 Number of length n+3 0..6 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247532 Number of length n+3 0..7 arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247534 Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247535 Number of length 3+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247536 Number of length 4+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

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A247537 Number of length 5+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

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