A036087 -id:A036087 - cp's OEIS frontend

A036088 Centered cube numbers: (n+1)^10 + n^10.

1, 1025, 60073, 1107625, 10814201, 70231801, 342941425, 1356217073, 4560526225, 13486784401, 35937424601, 87854788825, 199775856073, 427113146825, 865905045601, 1676162018401, 3115505528225

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^8 + 4n^7 + 18n^6 + 40n^5 + 56n^4 + 50n^3 + 27n^2 + 8n + 1), multiple of A001844(n). Semiprime for n in {2, 4, 7, 14, 19, 22, 32, 60, 65, 70, 87, 99, 102, 135, 137, ...}. - Jonathan Vos Post, Aug 26 2011

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A036085, A036087, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^10+n^10: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Total/@Partition[Range[0,20]^10,2,1] (* Harvey P. Dale, Aug 04 2019 *)

G.f.: -(x^8 + 1012*x^7 + 46828*x^6 + 408364*x^5 + 901990*x^4 + 408364*x^3 + 46828*x^2 + 1012*x + 1)*(1+x)^2 / (x-1)^11. - R. J. Mathar, Aug 27 2011

A036089 Centered cube numbers: (n+1)^11 + n^11.

Original entry on oeis.org

1, 2049, 179195, 4371451, 53022429, 411625181, 2340123799, 10567261335, 39970994201, 131381059609, 385311670611, 1028320041299, 2535168764725, 5841725563701, 12699321029039, 26241941903791, 51864082352049

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2*n+1) * (n^10 + 5*n^9 + 25*n^8 + 70*n^7 + 130*n^6 + 166*n^5 + 148*n^4 + 91*n^3 + 37*n^2 + 9*n + 1). - Jonathan Vos Post, Aug 26 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A008455, A036087, A036088, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^11+n^11: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Vec((1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12 + O(x^40)) \\ Colin Barker, Feb 06 2020

From Colin Barker, Feb 06 2020: (Start)
G.f.: (1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>11.
(End)

A036091 Centered cube numbers: (n+1)^13+n^13.

Original entry on oeis.org

1, 8193, 1602515, 68703187, 1287811989, 14281397141, 109949704423, 646644824295, 3091621642217, 12541865828329, 44522712143931, 141515917523003, 409868311971325, 1096589879846397, 2739909841613519

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n + 1) * (n^12 + 6n^11 + 36n^10 + 125n^9 + 295n^8 + 496n^7 + 610n^6 + 553n^5 + 367n^4 + 174n^3 + 56n^2 + 11n + 1). Semiprime for n in {1, 8, 15, 21, 86, 135, 141, 249, 260, 278, 323, 326, 363, ...}. - Jonathan Vos Post, Aug 26 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Cf. A036085, A036087, A036088, A036089, A036090.

[(n+1)^13+n^13: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

A036091:=n->(n + 1)^13 + n^13; seq(A036091(n), n=0..20); # Wesley Ivan Hurt, Apr 01 2014

Table[(n + 1)^13 + n^13, {n, 0, 20}] (* Wesley Ivan Hurt, Apr 01 2014 *)

A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

Original entry on oeis.org

1, 16385, 4799353, 273218425, 6371951081, 84467679721, 756587236945, 5076269583953, 27274838966065, 122876792454961, 479749833583241, 1663668298132105, 5221294850248153, 15049383211257305, 40304932850948641, 101250520063318561, 240435420597328865

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^12 + 6n^11 + 39n^10 + 140n^9 + 341n^8 + 590n^7 + 741n^6 + 680n^5 + 451n^4 + 210n^3 + 65n^2 + 12n + 1). Semiprime for n in {2, 5, 22, 24, 34, 35, 39, 84, 217, 220, 285, ...}. - Jonathan Vos Post, Aug 26 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^14+n^14: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

G.f.: -(x +1)^2*(x^12 +16368*x^11 +4520946*x^10 +193889840*x^9 +2377852335*x^8 +10465410528*x^7 +17505765564*x^6 +10465410528*x^5 +2377852335*x^4 +193889840*x^3 +4520946*x^2 +16368*x +1) / (x -1)^15. - Colin Barker, Feb 16 2015

A036095 Centered cube numbers: a(n) = (n+1)^17 + n^17.

Original entry on oeis.org

1, 131073, 129271235, 17309009347, 780119322309, 17689598897861, 249557173431943, 2484430327672455, 18928981513351817, 116677181699666569, 605447028499293771, 2724058135239730763, 10869027026121774925

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n + 1) * (n^16 + 8n^15 + 64n^14 + 308n^13 + 1036n^12 + 2576n^11 + 4900n^10 + 7274n^9 + 8518n^8 + 7896n^7 + 5776n^6 + 3300n^5 + 1444n^4 + 468n^3 + 106n^2 + 15n + 1). Semiprime for n in {1, 5, 21, 29, 33, ...}. - Jonathan Vos Post, Aug 27 2011

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A036092, A036093, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^17+n^17: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

Original entry on oeis.org

5, 13, 9, 25, 35, 17, 41, 91, 97, 33, 61, 189, 337, 275, 65, 85, 341, 881, 1267, 793, 129, 113, 559, 1921, 4149, 4825, 2315, 257, 145, 855, 3697, 10901, 19721, 18571, 6817, 513, 181, 1241, 6497, 24583, 62281, 94509, 72097, 20195, 1025, 221, 1729, 10657, 49575

Offset: 1

R. H. Hardin, with R. J. Mathar in the Sequence Fans Mailing List, Mar 30 2012

Table starts
...5....13.....25......41.......61.......85.......113.......145........181
...9....35.....91.....189......341......559.......855......1241.......1729
..17....97....337.....881.....1921.....3697......6497.....10657......16561
..33...275...1267....4149....10901....24583.....49575.....91817.....159049
..65...793...4825...19721....62281...164305....379793....793585....1531441
.129..2315..18571...94509...358061..1103479...2920695...6880121...14782969
.257..6817..72097..456161..2070241..7444417..22542017..59823937..143046721
.513.20195.281827.2215269.12030821.50431303.174571335.521638217.1387420489
Solutions are determined by the diagonal, extended with x(i,j) = (x(i,i)+x(j,j))/2 * (-1)^(i-j)

			Some solutions for n=3 k=4
.-2..1.-3..0....0.-1..0..1....4..0..1.-1....2.-1.-1.-2....3.-2..1..0
..1..0..2..1...-1..2.-1..0....0.-4..3.-3...-1..0..2..1...-2..1..0.-1
.-3..2.-4..1....0.-1..0..1....1..3.-2..2...-1..2.-4..1....1..0.-1..2
..0..1..1..2....1..0..1.-2...-1.-3..2.-2...-2..1..1..2....0.-1..2.-3

R. H. Hardin, Table of n, a(n) for n = 1..10000

cf. A179927
Column 1 is A000051(n+1)
Column 2 is A007689(n+1)
Column 3 is A074605(n+1)
Column 4 is A074611(n+1)
Column 5 is A074615(n+1)
Column 6 is A074619(n+1)
Column 7 is A074622(n+1)
Column 8 is A074624(n+1)
Row 1 is A001844
Row 2 is A005898
Row 3 is A008514
Row 4 is A008515
Row 5 is A008516
Row 6 is A036085
Row 7 is A036086
Row 8 is A036087

T(n,k)=k^(n+1)+(k+1)^(n+1)

cp's OEIS Frontend

A036088 Centered cube numbers: (n+1)^10 + n^10.

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A036089 Centered cube numbers: (n+1)^11 + n^11.

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A036091 Centered cube numbers: (n+1)^13+n^13.

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A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

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A036095 Centered cube numbers: a(n) = (n+1)^17 + n^17.

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Magma

A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

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