A074619 -id:A074619 - cp's OEIS frontend

A245807 a(n) = 7^n + 10^n.

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143

Offset: 0

Vincenzo Librandi, Aug 04 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (17,-70).

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

Magma
```
[7^n+10^n: n in [0..25]];
```

I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];

Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
E.g.f.: e^(7*x) + e^(10*x).
a(n) = 17*a(n-1)-70*a(n-2).
a(n) = A000420(n) + A011557(n).

A074520 1^n + 6^n + 7^n.

Original entry on oeis.org

3, 14, 86, 560, 3698, 24584, 164306, 1103480, 7444418, 50431304, 342941426, 2340123800, 16018069538, 109949704424, 756587236946, 5217746494520, 36054040477058, 249557173431944, 1729973554578866, 12008254925383640

Offset: 0

Robert G. Wilson v, Aug 23 2002

Index entries for linear recurrences with constant coefficients, signature (14,-55,42).

Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

A074520:=n->1^n + 6^n + 7^n; seq(A074520(n), n=0..100); # Wesley Ivan Hurt, Nov 11 2013

Mathematica
```
Table[1 + 6^n + 7^n, {n, 0, 20}]
```

G.f.:1/(1-x)+1/(1-6*x)+1/(1-7*x). E.g.f.: e^x+e^(6*x)+e^(7*x). [Mohammad K. Azarian, Dec 26 2008]
a(n) = 13*a(n-1) - 42*a(n-2) + 30, n>1. [Gary Detlefs, Jun 21 2010]
a(n) = A074619(n) + 1. - Michel Marcus, Nov 11 2013

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)

A221904 a(n) = 9^n + 10^n.

Original entry on oeis.org

2, 19, 181, 1729, 16561, 159049, 1531441, 14782969, 143046721, 1387420489, 13486784401, 131381059609, 1282429536481, 12541865828329, 122876792454961, 1205891132094649, 11853020188851841

Offset: 0

Vincenzo Librandi, Feb 06 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (19,-90).

Cf. A007689, A074611, A074615, A074619, A074622, A074624, A155872.

Magma
```
[9^n + 10^n: n in [0..30]];
```

CoefficientList[Series[1/(1-9*x) + 1/(1-10*x), {x, 0, 30}], x]
LinearRecurrence[{19,-90},{2,19},30] (* Harvey P. Dale, Nov 10 2017 *)

G.f.: 1/(1 - 9*x) + 1/(1 - 10*x).
E.g.f.: exp(9*x) + exp(10*x).
a(n) = 19*a(n-1) - 90*a(n-2), a(1)=2, a(2)=19.

A045600 Numbers k that divide 7^k + 6^k.

Original entry on oeis.org

1, 13, 169, 2197, 28561, 371293, 2684903, 4826809, 34903739, 62748517, 257734633, 453748607, 815730721, 3185696137, 3350550229, 5898731891, 10604499373, 41414049781, 42655053961, 43557152977, 76683514583

Offset: 1

David W. Wilson

nonn

Cf. A074619.

A220788 Numbers k such that 7^k + 6^k is prime.

Original entry on oeis.org

0, 1, 4, 16

Offset: 1

Vincenzo Librandi, Jan 10 2013

Next term is > 15000 if it exists.

Next term is > 100000 if it exists. - Michael S. Branicky, Oct 10 2024

Cf. A062573, A074619.

/* The program does not work for n>2700: */ [n: n in [0..1000]| IsPrime(7^n + 6^n)];

Join[{0, 1}, Select[2 Range[500], PrimeQ[7^# + 6^#] &]]

for(n=0, 1000, if(isprime(7^n + 6^n), print1(n, ", ")))

cp's OEIS Frontend

A245807 a(n) = 7^n + 10^n.

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Magma

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A074520 1^n + 6^n + 7^n.

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Maple

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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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Formula

A221904 a(n) = 9^n + 10^n.

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Author

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Programs

Magma

Mathematica

Formula

A045600 Numbers k that divide 7^k + 6^k.

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Author

Keywords

Crossrefs

A220788 Numbers k such that 7^k + 6^k is prime.

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Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI