A016973 -id:A016973 - cp's OEIS frontend

A016974 a(n) = (6*n + 5)^6.

15625, 1771561, 24137569, 148035889, 594823321, 1838265625, 4750104241, 10779215329, 22164361129, 42180533641, 75418890625, 128100283921, 208422380089, 326940373369, 496981290961, 735091890625, 1061520150601, 1500730351849, 2081951752609, 2839760855281, 3814697265625

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A016969 (6*n +5), A016970, A016971, A016972, A016973.

Subsequence of A001014 (n^6).

[(6*n+5)^6: n in [0..25]]; // Vincenzo Librandi, May 10 2011

(6Range[0,20]+5)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{15625,1771561,24137569,148035889,594823321,1838265625,4750104241},30] (* Harvey P. Dale, Apr 24 2025 *)

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^6 = A016970(n)^3 = A016971(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(5, 5/6)/5598720. (End)

A016975 a(n) = (6*n + 5)^7.

Original entry on oeis.org

78125, 19487171, 410338673, 3404825447, 17249876309, 64339296875, 194754273881, 506623120463, 1174711139837, 2488651484819, 4902227890625, 9095120158391, 16048523266853, 27136050989627, 44231334895529, 69833729609375, 107213535210701, 160578147647843, 235260548044817

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974.

Subsequence of A001015 (n^7).

[(6*n+5)^7: n in [0..25]]; // Vincenzo Librandi, May 11 2011

(6Range[0,20]+5)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{78125,19487171,410338673,3404825447,17249876309,64339296875,194754273881,506623120463},20] (* Harvey P. Dale, Jan 30 2013 *)

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Jan 30 2013
From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^7.
Sum_{n>=0} 1/a(n) = 138811*zeta(7)/279936 - 301*Pi^7/(1049760*sqrt(3)). (End)

A016976 a(n) = (6*n + 5)^8.

Original entry on oeis.org

390625, 214358881, 6975757441, 78310985281, 500246412961, 2251875390625, 7984925229121, 23811286661761, 62259690411361, 146830437604321, 318644812890625, 645753531245761, 1235736291547681, 2252292232139041, 3936588805702081, 6634204312890625, 10828567056280801

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974, A016975.

Subsequence of A001016 (n^8).

[(6*n+5)^8: n in [0..20]]; // Vincenzo Librandi, May 12 2011

Table[(6*n + 5)^8, {n, 0, 20}] (* Amiram Eldar, Apr 01 2022 *)

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^8 = A016970(n)^4 = A016972(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(7, 5/6)/8465264640. (End)

A016977 a(n) = (6*n + 5)^9.

Original entry on oeis.org

1953125, 2357947691, 118587876497, 1801152661463, 14507145975869, 78815638671875, 327381934393961, 1119130473102767, 3299763591802133, 8662995818654939, 20711912837890625, 45848500718449031, 95151694449171437, 186940255267540403, 350356403707485209, 630249409724609375

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A016969, A016970, A016971, A016972, A016973, A016974, A016975, A016976.

Subsequence of A001017.

[(6*n+5)^9: n in [0..35]]; // Vincenzo Librandi, May 13 2011

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^9 = A016971(n)^3.
Sum_{n>=0} 1/a(n) = 5028751*zeta(9)/10077696 - 15371*Pi^9/(529079040*sqrt(3)). (End)

A016978 a(n) = (6*n + 5)^10.

Original entry on oeis.org

9765625, 25937424601, 2015993900449, 41426511213649, 420707233300201, 2758547353515625, 13422659310152401, 52599132235830049, 174887470365513049, 511116753300641401, 1346274334462890625, 3255243551009881201, 7326680472586200649, 15516041187205853449

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974, A016975, A016976, A016977.

Subsequence of A008454 (n^10).

[(6*n+5)^10: n in [0..30]]; // Vincenzo Librandi, May 14 2011

(6*Range[0,20]+5)^10 (* Harvey P. Dale, Aug 26 2012 *)

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^10 = A016970(n)^5 = A016973(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(9, 5/6)/21941965946880. (End)

A016979 a(n) = (6*n + 5)^11.

Original entry on oeis.org

48828125, 285311670611, 34271896307633, 952809757913927, 12200509765705829, 96549157373046875, 550329031716248441, 2472159215084012303, 9269035929372191597, 30155888444737842659, 87507831740087890625, 231122292121701565271, 564154396389137449973

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974, A016975, A016976, A016977, A016978.

Subsequence of A008455 (n^11).

[(6*n+5)^11 : n in [0..20]]; // Vincenzo Librandi, May 17 2011

(6Range[0,20]+5)^11 (* or *) LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{48828125,285311670611,34271896307633,952809757913927,12200509765705829,96549157373046875,550329031716248441,2472159215084012303,9269035929372191597,30155888444737842659,87507831740087890625,231122292121701565271},20] (* Harvey P. Dale, Dec 17 2024 *)

a(n) = (6*n + 5)^11.
From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^11.
Sum_{n>=0} 1/a(n) = 181308931*zeta(11)/362797056 - 1261501*Pi^11/(428554022400*sqrt(3)). (End)

A016980 a(n) = (6*n + 5)^12.

Original entry on oeis.org

244140625, 3138428376721, 582622237229761, 21914624432020321, 353814783205469041, 3379220508056640625, 22563490300366186081, 116191483108948578241, 491258904256726154641, 1779197418239532716881, 5688009063105712890625, 16409682740640811134241, 43439888521963583647921

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974, A016975, A016976, A016977, A016978, A016979.

Subsequence of A008456 (n^12).

[(6*n+5)^12: n in [0..40]]; // Vincenzo Librandi, May 19 2011

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016969(n)^12 = A016970(n)^6 = A016971(n)^4 = A016972(n)^3 = A016974(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(11, 5/6)/86890185149644800. (End)

cp's OEIS Frontend

A016974 a(n) = (6*n + 5)^6.

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A016975 a(n) = (6*n + 5)^7.

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A016976 a(n) = (6*n + 5)^8.

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A016977 a(n) = (6*n + 5)^9.

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Magma

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A016978 a(n) = (6*n + 5)^10.

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Magma

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A016979 a(n) = (6*n + 5)^11.

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Magma

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A016980 a(n) = (6*n + 5)^12.

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