cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A207094 Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 3.

Original entry on oeis.org

3, 6, 12, 26, 55, 115, 239, 498, 1038, 2162, 4502, 9375, 19523, 40655, 84659, 176292, 367107, 764456, 1591886, 3314907, 6902887, 14374415, 29932954, 62331700, 129798109, 270288619, 562842849, 1172051097, 2440652442, 5082358916
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2012

Keywords

Comments

Column 2 of A207100.

Examples

			Some solutions for n=5:
..1....0....1....0....0....0....0....0....1....0....1....1....0....0....0....0
..2....1....2....1....1....0....0....2....1....0....2....2....1....1....0....0
..2....1....1....1....2....0....2....2....2....0....1....2....2....2....0....0
..1....2....1....2....2....0....2....1....2....1....0....1....1....1....0....0
..2....2....2....0....1....1....2....2....2....2....1....0....2....0....0....2

Links

Crossrefs

Cf. A207100.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-4) - a(n-6) - a(n-9).
Empirical g.f.: x*(3 + 2*x^3 - x^5 - x^8) / ((1 - x)*(1 - x - x^2 - x^3 - 2*x^4 - 2*x^5 - x^6 - x^7 - x^8)). - Colin Barker, Jun 18 2018

A207095 Number of 0..3 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 4.

Original entry on oeis.org

4, 10, 26, 68, 176, 458, 1193, 3103, 8069, 20982, 54556, 141854, 368847, 959072, 2493770, 6484280, 16860367, 43840173, 113992823, 296403114, 770704718, 2003979505, 5210729566, 13548892363, 35229708616, 91603972925, 238187830252
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Column 3 of A207100

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) +a(n-3) -3*a(n-4) +a(n-6) -2*a(n-9) +2*a(n-12) +a(n-13) -a(n-16)

A207096 Number of 0..4 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 5.

Original entry on oeis.org

5, 15, 45, 140, 441, 1382, 4322, 13511, 42238, 132051, 412840, 1290698, 4035218, 12615643, 39441343, 123308779, 385510576, 1205254047, 3768086810, 11780485818, 36830320820, 115145720853, 359989724116, 1125466066030, 3518638952555
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Column 4 of A207100

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) -2*a(n-3) +a(n-5) +2*a(n-8) -a(n-10) +3*a(n-11) -2*a(n-12) +a(n-13) -a(n-14) -2*a(n-15) +a(n-16) -2*a(n-17) +a(n-19) -3*a(n-21) +a(n-25)

A207097 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 6.

Original entry on oeis.org

6, 21, 75, 274, 989, 3579, 12964, 46952, 170076, 616065, 2231527, 8083084, 29278684, 106053662, 384149029, 1391469865, 5040201168, 18256685634, 66129616610, 239535602559, 867649138787, 3142810588438, 11383931537547, 41235032657415
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Column 5 of A207100

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-3) -5*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-7) +a(n-8) -6*a(n-9) -4*a(n-10) -6*a(n-11) +9*a(n-12) +2*a(n-13) -3*a(n-14) +2*a(n-15) +5*a(n-16) +7*a(n-17) -6*a(n-18) +a(n-19) -3*a(n-20) +2*a(n-21) +a(n-22) +3*a(n-23) -a(n-24) -4*a(n-25) +a(n-26) -2*a(n-27) +a(n-28) -a(n-29) +a(n-30) -a(n-31) -a(n-32) -a(n-36)

A207098 Number of 0..6 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 7.

Original entry on oeis.org

7, 28, 112, 462, 1904, 7868, 32531, 134517, 556259, 2300219, 9511719, 39332200, 162643507, 672550879, 2781080236, 11500107101, 47554350602, 196643061212, 813143132135, 3362446402726, 13904127534002, 57495269615906
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2012

Keywords

Examples

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

Links

Crossrefs

Column 6 of A207100.

Formula

Empirical: a(n) = 4*a(n-1) +3*a(n-2) -9*a(n-3) -8*a(n-4) +12*a(n-5) +11*a(n-6) -6*a(n-7) +5*a(n-8) -2*a(n-9) -17*a(n-10) +3*a(n-11) -4*a(n-12) -4*a(n-13) +a(n-14) -2*a(n-15) +9*a(n-16) -12*a(n-17) -a(n-18) +10*a(n-19) -19*a(n-20) -9*a(n-21) +7*a(n-22) -4*a(n-23) -3*a(n-24) +4*a(n-25) +14*a(n-26) +5*a(n-28) +11*a(n-29) +a(n-30) -a(n-31) -a(n-32) +8*a(n-33) +2*a(n-34) -a(n-35) +5*a(n-36) -2*a(n-37) -2*a(n-38) -a(n-40) -3*a(n-42) -a(n-43) -a(n-44) -a(n-49).

A207099 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 8.

Original entry on oeis.org

8, 36, 164, 760, 3504, 16224, 75114, 347794, 1610482, 7457403, 34531926, 159901992, 740434409, 3428619670, 15876397382, 73516462261, 340421698733, 1576339895161, 7299321618669, 33799877958800, 156512044508653, 724736938606683
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Column 7 of A207100

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) +6*a(n-2) -9*a(n-3) -27*a(n-4) +49*a(n-6) +41*a(n-7) -15*a(n-8) -74*a(n-9) -21*a(n-10) +24*a(n-11) +14*a(n-12) +10*a(n-13) -108*a(n-14) -72*a(n-15) -91*a(n-16) +24*a(n-17) +77*a(n-18) +126*a(n-19) +102*a(n-20) +90*a(n-21) +192*a(n-22) +188*a(n-23) +162*a(n-24) +165*a(n-25) -12*a(n-26) -24*a(n-27) -446*a(n-28) -378*a(n-29) -335*a(n-30) -191*a(n-31) -101*a(n-32) -111*a(n-33) -83*a(n-34) -31*a(n-35) +165*a(n-36) +208*a(n-37) +237*a(n-38) +191*a(n-39) +24*a(n-40) +29*a(n-41) -12*a(n-42) +11*a(n-43) -22*a(n-44) -5*a(n-45) +20*a(n-46) +6*a(n-47) -23*a(n-48) -35*a(n-49) -31*a(n-50) -26*a(n-51) +2*a(n-52) +2*a(n-53) +3*a(n-54) -a(n-55) +a(n-56) +a(n-57) -a(n-58) +a(n-60) +a(n-61) +a(n-62) +a(n-63)

A207101 Number of 0..n arrays x(0..3) of 4 elements with each no smaller than the sum of its two previous neighbors modulo (n+1).

Original entry on oeis.org

8, 26, 68, 140, 274, 462, 760, 1158, 1720, 2431, 3392, 4550, 6048, 7825, 10032, 12597, 15726, 19285, 23540, 28343, 33968, 40250, 47536, 55575, 64792, 74916, 86380, 98890, 112970, 128216, 145248, 163636, 184008, 205905, 230064, 255892, 284240, 314483
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2012

Keywords

Comments

Row 4 of A207100.

Examples

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

Links

Crossrefs

Cf. A207100.

Formula

Empirical: a(n) = 3*a(n-2) + 2*a(n-3) - 3*a(n-4) - 6*a(n-5) + 6*a(n-7) + 3*a(n-8) - 2*a(n-9) - 3*a(n-10) + a(n-12).
Empirical g.f.: x*(8 + 26*x + 44*x^2 + 46*x^3 + 42*x^4 + 32*x^5 + 18*x^6 + 4*x^7 - 2*x^8 - 3*x^9 + x^11) / ((1 - x)^5*(1 + x)^3*(1 + x + x^2)^2). - Colin Barker, Jun 19 2018

A207102 Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its two previous neighbors modulo (n+1).

Original entry on oeis.org

12, 55, 176, 441, 989, 1904, 3504, 5925, 9652, 14850, 22390, 32305, 45920, 63323, 86112, 114393, 150567, 194218, 248704, 313495, 392480, 485024, 596300, 724705, 876876, 1051011, 1254512, 1485177, 1752481, 2052448, 2396864, 2781317, 3218508
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2012

Keywords

Comments

Row 5 of A207100.

Examples

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

Links

Crossrefs

Cf. A207100.

Formula

Empirical: a(n) = -3*a(n-1) -2*a(n-2) +5*a(n-3) +12*a(n-4) +9*a(n-5) -3*a(n-6) -14*a(n-7) -19*a(n-8) -17*a(n-9) -3*a(n-10) +20*a(n-11) +32*a(n-12) +20*a(n-13) -3*a(n-14) -17*a(n-15) -19*a(n-16) -14*a(n-17) -3*a(n-18) +9*a(n-19) +12*a(n-20) +5*a(n-21) -2*a(n-22) -3*a(n-23) -a(n-24).

A207103 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its two previous neighbors modulo (n+1).

Original entry on oeis.org

18, 115, 458, 1382, 3579, 7868, 16224, 30390, 54294, 90959, 148204, 229944, 349580, 513531, 740976, 1041114, 1444791, 1960021, 2632938, 3474205, 4543704, 5855409, 7493700, 9466310, 11887746, 14768802, 18248930, 22339541, 27226927, 32903121
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Row 6 of A207100

Examples

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

Links

Formula

Empirical: a(n) = -3*a(n-1) -5*a(n-2) -5*a(n-3) -3*a(n-4) +2*a(n-5) +11*a(n-6) +21*a(n-7) +27*a(n-8) +25*a(n-9) +16*a(n-10) -3*a(n-11) -28*a(n-12) -52*a(n-13) -66*a(n-14) -67*a(n-15) -51*a(n-16) -16*a(n-17) +27*a(n-18) +69*a(n-19) +99*a(n-20) +111*a(n-21) +93*a(n-22) +52*a(n-23) -52*a(n-25) -93*a(n-26) -111*a(n-27) -99*a(n-28) -69*a(n-29) -27*a(n-30) +16*a(n-31) +51*a(n-32) +67*a(n-33) +66*a(n-34) +52*a(n-35) +28*a(n-36) +3*a(n-37) -16*a(n-38) -25*a(n-39) -27*a(n-40) -21*a(n-41) -11*a(n-42) -2*a(n-43) +3*a(n-44) +5*a(n-45) +5*a(n-46) +3*a(n-47) +a(n-48)

A207104 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its two previous neighbors modulo (n+1).

Original entry on oeis.org

27, 239, 1193, 4322, 12964, 32531, 75114, 155922, 305362, 557095, 980755, 1636154, 2659934, 4162116, 6371316, 9468167, 13851960, 19762261, 27846149, 38462192, 52544085, 70608666, 94060846, 123500085, 160955964, 207261711, 265103651
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Row 7 of A207100

Examples

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

Links

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