A270870 -id:A270870 - cp's OEIS frontend

A270871 a(n) = n^7 + 6n^6 + 26n^5 + 73n^4 + 152n^3 + 222n^2 + 203n + 8.

8, 691, 5030, 25511, 100372, 324323, 898706, 2206135, 4914656, 10116467, 19506238, 35604071, 62028140, 103822051, 167841962, 263208503, 401828536, 598991795, 874047446, 1251165607, 1760188868, 2437578851, 3327462850, 4482785591, 5966571152, 7853300083

Offset: 0

Vincenzo Librandi, Apr 03 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 7th row).
Index entries for linear recurrences with constant coefficients, signature (8,-28, 56,-70,56,-28,8,-1).

Cf. A270867, A270868. A270869, A270870.

[n^7+6*n^6+26*n^5+73*n^4+152*n^3+222*n^2+203*n+8: n in [0..40]];

Table[n^7 + 6 n^6 + 26 n^5 + 73 n^4 + 152 n^3 + 222 n^2 + 203 n + 8, {n, 0, 40}]
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{8,691,5030,25511,100372,324323,898706,2206135},30] (* Harvey P. Dale, Dec 17 2023 *)

x='x+O('x^99); Vec((8+627*x-274*x^2+4171*x^3-1012*x^4+1897*x^5-450*x^6+73*x^7) / (1-x)^8) \\ Altug Alkan, Apr 03 2016

G.f.: (8 + 627*x - 274*x^2 + 4171*x^3 - 1012*x^4 + 1897*x^5 - 450*x^6 + 73*x^7)/(1 - x)^8.

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).

A270872 a(n) = n^8 + 7n^7 + 34n^6 + 111n^5 + 275n^4 + 511n^3 + 703n^2 + 623*n + 13.

Original entry on oeis.org

13, 2278, 19439, 117910, 550009, 2072078, 6584443, 18269614, 45445445, 103390294, 218437543, 433677158, 816642289, 1469399230, 2541499379, 4246292158, 6881138173, 10852102214, 16703746015, 25154681014, 37139581673, 53858400238, 76833564139, 107975977550

Offset: 0

Vincenzo Librandi, Apr 04 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 8th row).
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A270867, A270868, A270869, A270870, A270871.

[n^8+7*n^7+34*n^6+111*n^5+275*n^4+511*n^3+703*n^2+623*n+13: n in [0..40]];

Table[n^8 + 7 n^7 + 34 n^6 + 111 n^5 + 275 n^4 + 511 n^3 + 703 n^2 + 623 n + 13, {n, 0, 40}]
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{13,2278,19439,117910,550009,2072078,6584443,18269614,45445445},30] (* Harvey P. Dale, Jan 14 2023 *)

x='x+O('x^99); Vec((13+2161*x-595*x^2+23875*x^3-1091*x^4+19271*x^5-4997*x^6+1909*x^7-226*x^8)/(1-x)^9) \\ Altug Alkan, Apr 04 2016

G.f.: (13+2161*x-595*x^2+23875*x^3-1091*x^4+19271*x^5-4997*x^6+1909*x^7-226*x^8)/(1-x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).

A270873 a(n) = n^9 + 8n^8 + 43n^7 + 159n^6 + 452n^5 + 997n^4 + 1725n^3 + 2272n^2 + 1990n + 21.

Original entry on oeis.org

21, 7668, 75545, 545730, 3015021, 13239896, 48243393, 151298070, 420233285, 1056651996, 2446142121, 5282430218, 10751650845, 20796493440, 38483939921, 68504620446, 117836491893, 196610583620, 319221957945, 505734798546, 783636668621, 1190003472168

Offset: 0

Vincenzo Librandi, Apr 04 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 9th row).
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A270867, A270868, A270869, A270870, A270871, A270872.

[n^9+8*n^8+43*n^7+159*n^6+452*n^5+997*n^4+1725*n^3+2272*n^2+1990*n+21: n in [0..40]];

Table[n^9 + 8 n^8 + 43 n^7 + 159 n^6 + 452 n^5 + 997 n^4 + 1725 n^3 + 2272 n^2 + 1990 n + 21, {n, 0, 40}]
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{21,7668,75545,545730,3015021,13239896,48243393,151298070,420233285,1056651996},30] (* Harvey P. Dale, Dec 02 2018 *)

my(x='x+O('x^99)); Vec((21+7458*x-190*x^2+132820*x^3+41496*x^4+187124*x^5-30698*x^6+30660*x^7-6565*x^8+754*x^9)/(1-x)^10) \\ Altug Alkan, Apr 04 2016

G.f.: (21+7458*x-190*x^2+132820*x^3+41496*x^4+187124*x^5-30698*x^6+30660*x^7-6565*x^8+754*x^9)/(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).

A270874 a(n) = n^10 + 9n^9 + 53n^8 + 218n^7 + 695n^6 + 1754n^5 + 3572n^4 + 5854n^3 + 7510n^2 + 6559*n + 34.

Original entry on oeis.org

34, 26259, 294888, 2528263, 16531326, 84603579, 353479684, 1252968303, 3885899418, 10799026531, 27392790624, 64342966359, 141552806518, 294334006923, 582732259836, 1105171977919, 2017898582034, 3562049183283, 6100587181528, 10167796877991, 16534554287214

Offset: 0

Vincenzo Librandi, Apr 05 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 10th row).
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A270867, A270868, A270869, A270870, A270871, A270872, A270873.

[n^10 +9*n^9 +53*n^8 +218*n^7 +695*n^6 +1754*n^5 +3572*n^4 +5854*n^3 +7510*n^2 +6559*n +34: n in [0..30]];

Table[n^10 + 9 n^9 + 53 n^8 + 218 n^7 + 695 n^6 + 1754 n^5 + 3572 n^4 + 5854 n^3 + 7510 n^2 + 6559 n + 34, {n, 0, 30}]
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{34,26259,294888,2528263,16531326,84603579,353479684,1252968303,3885899418,10799026531,27392790624},30] (* Harvey P. Dale, Apr 10 2017 *)

x='x+O('x^99); Vec((34+25885*x+7909*x^2+723130*x^3+617758*x^4+1806700*x^5+ 96940*x^6+428806*x^7-101360*x^8+25527*x^9-2529*x^10)/(1-x)^11) \\ Altug Alkan, Apr 05 2016

G.f.: (34+25885*x+7909*x^2+723130*x^3+617758*x^4+1806700*x^5+ 96940*x^6+428806*x^7-101360*x^8+25527*x^9-2529*x^10)/(1-x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

cp's OEIS Frontend

A270871 a(n) = n^7 + 6*n^6 + 26*n^5 + 73*n^4 + 152*n^3 + 222*n^2 + 203*n + 8.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A270872 a(n) = n^8 + 7*n^7 + 34*n^6 + 111*n^5 + 275*n^4 + 511*n^3 + 703*n^2 + 623*n + 13.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A270873 a(n) = n^9 + 8*n^8 + 43*n^7 + 159*n^6 + 452*n^5 + 997*n^4 + 1725*n^3 + 2272*n^2 + 1990*n + 21.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A270874 a(n) = n^10 + 9*n^9 + 53*n^8 + 218*n^7 + 695*n^6 + 1754*n^5 + 3572*n^4 + 5854*n^3 + 7510*n^2 + 6559*n + 34.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A270871 a(n) = n^7 + 6n^6 + 26n^5 + 73n^4 + 152n^3 + 222n^2 + 203n + 8.

A270872 a(n) = n^8 + 7n^7 + 34n^6 + 111n^5 + 275n^4 + 511n^3 + 703n^2 + 623*n + 13.

A270873 a(n) = n^9 + 8n^8 + 43n^7 + 159n^6 + 452n^5 + 997n^4 + 1725n^3 + 2272n^2 + 1990n + 21.

A270874 a(n) = n^10 + 9n^9 + 53n^8 + 218n^7 + 695n^6 + 1754n^5 + 3572n^4 + 5854n^3 + 7510n^2 + 6559*n + 34.