A123656 -id:A123656 - cp's OEIS frontend

A123659 a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

6, 18001, 4862512, 269750529, 6115250626, 78434755921, 678546021756, 4399254736897, 22880667197854, 100011001010001, 379778130741736, 1283985544700161, 3937524853545882, 11112316748827729, 29193541130581876

Offset: 1

Jonathan Vos Post, Oct 05 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1 + n^4 + n^6 + n^9 + n^10 + n^14: n in [1..25]]; // G. C. Greubel, Oct 17 2017

Table[1 + n^4 + n^6 + n^9 + n^10 + n^14, {n, 1, 50}] (* G. C. Greubel, Oct 17 2017 *)

for(n=1,25, print1(1 + n^4 + n^6 + n^9 + n^10 + n^14, ", ")) \\ G. C. Greubel, Oct 17 2017

a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

A123657 a(n) = 1 + n^4 + n^6 + n^9.

Original entry on oeis.org

4, 593, 20494, 266497, 1969376, 10125649, 40473658, 134483969, 387958492, 1001010001, 2359733894, 5162787073, 10609354744, 20668614737, 38454800626, 68736319489, 118612097588, 198393407569, 322734873982, 512064160001

Offset: 1

Jonathan Vos Post, Oct 04 2006

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

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1 + n^4 + n^6 + n^9: n in [1..25]]; // G. C. Greubel, Oct 17 2017

Table[1 + n^4 + n^6 + n^9, {n, 1, 50}] (* G. C. Greubel, Oct 17 2017 *)

a(n)=n^9+n^6+n^4+1 \\ Charles R Greathouse IV, Oct 16 2015

a(n) = 1 + n^4 + n^6 + n^9 = 1001010001 (base n).

G.f.: -x*(x^9 -8*x^8 -406*x^7 -14592*x^6 -88496*x^5 -156316*x^4 -87762*x^3 -14744*x^2 -553*x -4)/(x-1)^10. - Colin Barker, May 27 2012

A123665 a(n) = Sum_{k=1..21} n^A001358(k).

Original entry on oeis.org

22, 471260364628084305, 6457022669043550542502557676, 105149403852520725445003265581519105, 41911381174488637014293971538580334000626

Offset: 1

Jonathan Vos Post, Oct 04 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001358, A002523, A091940, A123177, A123656-A123665.

[1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 +
n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 + n^55 + n^57 + n^58: n in [1..50]]; // G. C. Greubel, Oct 26 2017

Table[1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 +
  n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 +
  n^55 + n^57 + n^58, {n, 1, 50}] (* G. C. Greubel, Oct 26 2017 *)

for(n=1,50, print1(1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 + n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 + n^55 + n^57 + n^58, ", ")) \\ G. C. Greubel, Oct 26 2017

a(n) = 1 +n^4 +n^6 +n^9 +n^10 +n^14 +n^15 +n^21 +n^22 +n^25 +n^26 + n^33 +n^34 +n^35 +n^38 +n^39 +n^46 +n^49 +n^51 +n^55 +n^57 +n^58.

Better name from Joerg Arndt, May 23 2021

A123658 a(n) = 1 + n^4 + n^6 + n^9 + n^10.

Original entry on oeis.org

5, 1617, 79543, 1315073, 11735001, 70591825, 322948907, 1208225793, 3874742893, 11001010001, 28297158495, 67080151297, 148467846593, 309923269713, 615105191251, 1168247947265, 2134605998037, 3768860634193, 6453801131783, 10752064160001, 17474246985385

Offset: 1

Jonathan Vos Post, Oct 04 2006

			a(40) = 1+40^(A001358(1))+40^(A001358(2))+40^(A001358(3))+40^(A001358(4)) = 1+40^4+40^6+40^9+40^10 = 10747908098560001.

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

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1+n^4+n^6+n^9+n^10: n in [0..50]]; // G. C. Greubel, Oct 17 2017

Table[1+n^4+n^6+n^9+n^10, {n,1,50}] (* G. C. Greubel, Oct 17 2017 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{5,1617,79543,1315073,11735001,70591825,322948907,1208225793,3874742893,11001010001,28297158495},30] (* Harvey P. Dale, Jul 11 2025 *)

a(n)=1+n^4+n^6+n^9+n^10 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 1 + n^4 + n^6 + n^9 + n^10.

G.f.: x*(x^10 -8*x^9 +615*x^8 +33654*x^7 +381288*x^6 +1242534*x^5 +1378908*x^4 +528210*x^3 +62031*x^2 +1562*x +5)/(1-x)^11. - Colin Barker, May 27 2012

A123238 A polynomial of degree 130.

Original entry on oeis.org

32, 1425203755583399996168049966590022914305, 106693983773666239196515949681928803974352131646102553502213120, 1854935026981753007730687157925149063119367096762979743090469098299990573383681

Offset: 1

Jonathan Vos Post, Oct 06 2006

Cf. A014612 (triprimes), A123656-A123665.

a(n) = 1 + n^8 + n^12 + n^18 + n^20 + n^27 + n^28 + n^30 + n^42 + n^44 + n^45 + n^50 + n^52 + n^63 + n^66 + n^68 + n^70 + n^75 + n^76 + n^78 + n^92 + n^98 + n^99 + n^102 + n^105 + n^110 + n^114 + n^116 + n^117 + n^124 + n^125 + n^130 = + / - (n^2 + 1) * (n^128 - n^126 + n^124 + n^123 - n^121 + n^119 - n^117 + 2n^115 + n^114 - 2n^113 + 2n&111 - 2n^109 + n^108 + 2n^107 - n^106 - 2n^105 + n^104 + 3n^103 - n^102 - 3n^101 + 2n^100 + 3n^99 - 2n^98 - 2n^97 + 3n^96 + 2n^95 - 3n^94 - 2n^93 + 3n^92 + 2n^91 - 2n^90 - 2n^89 + 2n^88 + 2n^87 - 2n^86 - 2n^85 + 2n^84 + 2n^83 - 2n^82 - 2n^81 + 2n^80 + 2n^79 - 2n^78 - 2n^77 + 3n^76 + 2n^75 - 2n^74 - n^73 + 2n^72 + n^71 - 2n^70 - n^69 + 3n^68 + n^67 - 2n^66 - n^65 + 3n^64 + n^63 - 3n^62 + 3n^60 - 3n^58 + 3n^56 - 3n^54 + 3n^52 - 2n^50 + 3n^48 - 3n^46 + 3n^44 + n^43 - 2n^42 - n^41 + 3n^40 + n^39 - 3n^38 - n^37 + 3n^36 + n^35 - 3n^34 - n^33 + 3n^32 + n^31 - 3n^30 - n^29 + 4n^28 + n^27 - 3n^26 + 3n^24 - 3n^22 + 3n^20 - 2n^18 + 3n^16 - 3n^14 + 3n^12 - 2n^10 + 2n^8 - n^6 + n^4 - n^2 + 1).

cp's OEIS Frontend

A123659 a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

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A123657 a(n) = 1 + n^4 + n^6 + n^9.

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A123665 a(n) = Sum_{k=1..21} n^A001358(k).

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A123658 a(n) = 1 + n^4 + n^6 + n^9 + n^10.

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A123238 A polynomial of degree 130.

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